Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The value of $not stretchy sum from r equals 0 to n of open parentheses a plus r plus a r close parentheses open parentheses negative a close parentheses to the power of r end exponent$ is equal to

${(- 1)}^{n} [(n + 1) a^{n + 1} - a]$
${(- 1)}^{n} (n + 1) a^{n + 1}$
${(- 1)}^{n} \frac{(n + 2) a^{n + 1}}{2}$
${(- 1)}^{n} \frac{n a^{n}}{2}$

The correct answer is: $open parentheses negative 1 close parentheses to the power of n end exponent open parentheses n plus 1 close parentheses a to the power of n plus 1 end exponent$

$T subscript r end subscript equals r open parentheses negative a close parentheses to the power of r end exponent plus open parentheses r plus 1 close parentheses a left parenthesis negative a right parenthesis to the power of r end exponent$
$equals r open parentheses negative a close parentheses to the power of r end exponent minus open parentheses r plus 1 close parentheses open parentheses negative a close parentheses to the power of r plus 1 end exponent$
$equals v subscript r end subscript minus v subscript r plus 1 end subscript$ (say)
So,
$not stretchy sum from r equals 0 to n of T subscript r end subscript equals not stretchy sum from r equals 0 to n of left parenthesis v subscript r end subscript minus v subscript r plus 1 end subscript right parenthesis$
$equals v subscript 0 end subscript minus v subscript n plus 1 end subscript$
$equals negative open parentheses n plus 1 close parentheses left parenthesis negative a right parenthesis to the power of n plus 1 end exponent$

Related Questions to study

The sum of series $1 plus fraction numerator 4 over denominator 5 end fraction plus fraction numerator 7 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 10 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity$ is

The sum of series $1 plus fraction numerator 4 over denominator 5 end fraction plus fraction numerator 7 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 10 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity$ is

If $t subscript n end subscript equals fraction numerator 1 over denominator 4 end fraction open parentheses n plus 2 close parentheses left parenthesis n plus 3 right parenthesis$ for $n equals 1 comma blank 2 comma blank 3 comma blank horizontal ellipsis comma blank$ then $fraction numerator 1 over denominator t subscript 1 end subscript end fraction plus fraction numerator 1 over denominator t subscript 2 end subscript end fraction plus fraction numerator 1 over denominator t subscript 3 end subscript end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator t subscript 2003 end subscript end fraction equals$

If $t subscript n end subscript equals fraction numerator 1 over denominator 4 end fraction open parentheses n plus 2 close parentheses left parenthesis n plus 3 right parenthesis$ for $n equals 1 comma blank 2 comma blank 3 comma blank horizontal ellipsis comma blank$ then $fraction numerator 1 over denominator t subscript 1 end subscript end fraction plus fraction numerator 1 over denominator t subscript 2 end subscript end fraction plus fraction numerator 1 over denominator t subscript 3 end subscript end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator t subscript 2003 end subscript end fraction equals$

The sum to 50 terms of the series $1 plus 2 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses plus 3 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses to the power of 2 end exponent plus horizontal ellipsis$ is given by

The sum to 50 terms of the series $1 plus 2 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses plus 3 open parentheses 1 plus fraction numerator 1 over denominator 50 end fraction close parentheses to the power of 2 end exponent plus horizontal ellipsis$ is given by

parallel

The line $x plus y equals 1$ meets $x$ -axis at $A$ and $y$ -axis at $B comma blank P$ is the mid-point of $A B$ ;
$P subscript 1 end subscript$ is the foot of the perpendicular from $P$ to $O A$ :
$M subscript 1 end subscript$ is that of $P subscript 1 end subscript$ from $O P$ ; $P subscript 2 end subscript$ is that of $M subscript 1 end subscript$ from $O A$ ; $M subscript 2 end subscript$ is that of $P subscript 2 end subscript$ from $O P$ ; $P subscript 3 end subscript$ is that of $M subscript 2 end subscript$ from $O A$ ; and so on.
If $P subscript n end subscript$ denotes the $n to the power of t h end exponent$ foot of the perpendicular on $O A$ : then $O P subscript n end subscript$ is

The line $x plus y equals 1$ meets $x$ -axis at $A$ and $y$ -axis at $B comma blank P$ is the mid-point of $A B$ ;
$P subscript 1 end subscript$ is the foot of the perpendicular from $P$ to $O A$ :
$M subscript 1 end subscript$ is that of $P subscript 1 end subscript$ from $O P$ ; $P subscript 2 end subscript$ is that of $M subscript 1 end subscript$ from $O A$ ; $M subscript 2 end subscript$ is that of $P subscript 2 end subscript$ from $O P$ ; $P subscript 3 end subscript$ is that of $M subscript 2 end subscript$ from $O A$ ; and so on.
If $P subscript n end subscript$ denotes the $n to the power of t h end exponent$ foot of the perpendicular on $O A$ : then $O P subscript n end subscript$ is
Maths-General

Let $a element of left parenthesis 0 comma blank 1 right square bracket$ satisfies the equation $a to the power of 2008 end exponent minus 2 a plus 1 equals 0$ and $S equals 1 plus a plus a to the power of 2 end exponent plus... plus a to the power of 2007 end exponent$ . Sum of all possible value(s) of $S$ , is

Let $a element of left parenthesis 0 comma blank 1 right square bracket$ satisfies the equation $a to the power of 2008 end exponent minus 2 a plus 1 equals 0$ and $S equals 1 plus a plus a to the power of 2 end exponent plus... plus a to the power of 2007 end exponent$ . Sum of all possible value(s) of $S$ , is

The maximum sum of the series $20 plus 19 fraction numerator 1 over denominator 3 end fraction plus 18 fraction numerator 2 over denominator 3 end fraction plus horizontal ellipsis$ is

The maximum sum of the series $20 plus 19 fraction numerator 1 over denominator 3 end fraction plus 18 fraction numerator 2 over denominator 3 end fraction plus horizontal ellipsis$ is

parallel

The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, then common ratio of the G.P. is

The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, then common ratio of the G.P. is

If $a comma blank b comma$ and $c$ are in A.P. and $b minus a comma blank c minus b$ and $a$ are in G.P., then $a colon b colon c$ is

If $a comma blank b comma$ and $c$ are in A.P. and $b minus a comma blank c minus b$ and $a$ are in G.P., then $a colon b colon c$ is

The coefficient of $x to the power of 49 end exponent$ in the product $open parentheses x minus 1 close parentheses open parentheses x minus 3 close parentheses midline horizontal ellipsis left parenthesis x minus 99 right parenthesis$ is

The coefficient of $x to the power of 49 end exponent$ in the product $open parentheses x minus 1 close parentheses open parentheses x minus 3 close parentheses midline horizontal ellipsis left parenthesis x minus 99 right parenthesis$ is

parallel

If $t subscript n end subscript$ denotes the $n to the power of t h end exponent$ term of the series $2 plus 3 plus 6 plus 11 plus 18 plus horizontal ellipsis$ then $t subscript 50 end subscript$ is

If $t subscript n end subscript$ denotes the $n to the power of t h end exponent$ term of the series $2 plus 3 plus 6 plus 11 plus 18 plus horizontal ellipsis$ then $t subscript 50 end subscript$ is

An infinite GP has first term $x$ and sum 5, then

An infinite GP has first term $x$ and sum 5, then

If $a comma blank b$ and $c$ are in A.P. then $a to the power of 3 end exponent plus c to the power of 3 end exponent minus 8 b to the power of 3 end exponent$ is equal to

If $a comma blank b$ and $c$ are in A.P. then $a to the power of 3 end exponent plus c to the power of 3 end exponent minus 8 b to the power of 3 end exponent$ is equal to

parallel

$A B C$ is a right-angled triangle in which $angle B equals 90 degree$ and $B C equals a$ . If $n$ points $L subscript 1 end subscript comma L subscript 2 end subscript comma horizontal ellipsis comma L subscript n end subscript$ on $A B$ is divided in $n plus 1$ equals parts and $L subscript 1 end subscript M subscript 1 end subscript comma L subscript 2 end subscript M subscript 2 end subscript comma blank horizontal ellipsis comma blank L subscript n end subscript M subscript n end subscript$ are line segments parallel to $B C$ and $M subscript 1 end subscript comma M subscript 2 end subscript comma horizontal ellipsis comma M subscript n end subscript$ are on $A C$ , then the sum of the lengths of $L subscript 1 end subscript M subscript 1 end subscript comma blank L subscript 2 end subscript M subscript 2 end subscript comma horizontal ellipsis comma L subscript n end subscript M subscript n end subscript$ is

$A B C$ is a right-angled triangle in which $angle B equals 90 degree$ and $B C equals a$ . If $n$ points $L subscript 1 end subscript comma L subscript 2 end subscript comma horizontal ellipsis comma L subscript n end subscript$ on $A B$ is divided in $n plus 1$ equals parts and $L subscript 1 end subscript M subscript 1 end subscript comma L subscript 2 end subscript M subscript 2 end subscript comma blank horizontal ellipsis comma blank L subscript n end subscript M subscript n end subscript$ are line segments parallel to $B C$ and $M subscript 1 end subscript comma M subscript 2 end subscript comma horizontal ellipsis comma M subscript n end subscript$ are on $A C$ , then the sum of the lengths of $L subscript 1 end subscript M subscript 1 end subscript comma blank L subscript 2 end subscript M subscript 2 end subscript comma horizontal ellipsis comma L subscript n end subscript M subscript n end subscript$ is

Consider an infinite geometric series with first term $a$ and common ratio $r$ . If its sum is 4 and the second term is 3/4, then

Consider an infinite geometric series with first term $a$ and common ratio $r$ . If its sum is 4 and the second term is 3/4, then

$stack lim with n rightwards arrow infinity below invisible function application not stretchy sum from r equals 1 to n of fraction numerator r over denominator 1 cross times 3 cross times 5 cross times 7 cross times 9 cross times midline horizontal ellipsis cross times left parenthesis 2 r plus 1 right parenthesis end fraction blank$ is equal to

$stack lim with n rightwards arrow infinity below invisible function application not stretchy sum from r equals 1 to n of fraction numerator r over denominator 1 cross times 3 cross times 5 cross times 7 cross times 9 cross times midline horizontal ellipsis cross times left parenthesis 2 r plus 1 right parenthesis end fraction blank$ is equal to

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.