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 sum of $fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 times 2 to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator 5 times 2 to the power of 5 end exponent end fraction plus midline horizontal ellipsis infinity$ is

${l o g}_{e} \sqrt{\frac{3}{2}}$
${l o g}_{e} \sqrt{3}$
${l o g}_{e} \sqrt{\frac{1}{2}}$
${l o g}_{e} 3$

The correct answer is: $l o g subscript e end subscript invisible function application square root of 3$

$text Sum of end text fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 3 end fraction times fraction numerator 1 over denominator 2 to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator 5 end fraction times fraction numerator 1 over denominator 2 to the power of 5 end exponent end fraction plus midline horizontal ellipsis infinity$
$table row cell equals fraction numerator 1 over denominator 2 end fraction open square brackets 1 plus fraction numerator 1 over denominator 3 end fraction times fraction numerator 1 over denominator 2 to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 5 end fraction times fraction numerator 1 over denominator 2 to the power of 4 end exponent end fraction plus midline horizontal ellipsis infinity close square brackets equals fraction numerator 1 over denominator 2 end fraction times l o g subscript e end subscript invisible function application open parentheses fraction numerator 1 plus fraction numerator 1 over denominator 2 end fraction over denominator 1 minus fraction numerator 1 over denominator 2 end fraction end fraction close parentheses equals fraction numerator 1 over denominator 2 end fraction times l o g subscript e end subscript invisible function application open parentheses fraction numerator 3 divided by 2 over denominator 1 divided by 2 end fraction close parentheses end cell row cell equals l o g subscript e end subscript invisible function application square root of 3 end cell end table$

Related Questions to study

$1 plus fraction numerator 1 plus 2 over denominator 2 factorial end fraction plus fraction numerator 1 plus 2 plus 3 over denominator 3 factorial end fraction plus fraction numerator 1 plus 2 plus 3 plus 4 over denominator 4 factorial end fraction plus midline horizontal ellipsis infinity equals$

$1 plus fraction numerator 1 plus 2 over denominator 2 factorial end fraction plus fraction numerator 1 plus 2 plus 3 over denominator 3 factorial end fraction plus fraction numerator 1 plus 2 plus 3 plus 4 over denominator 4 factorial end fraction plus midline horizontal ellipsis infinity equals$

The sum of the series $1 times 3 to the power of 2 end exponent plus 2 times 5 to the power of 2 end exponent plus 3 times 7 to the power of 2 end exponent plus midline horizontal ellipsis$ up to 20 terms is

The sum of the series $1 times 3 to the power of 2 end exponent plus 2 times 5 to the power of 2 end exponent plus 3 times 7 to the power of 2 end exponent plus midline horizontal ellipsis$ up to 20 terms is

$text If the end text left parenthesis m plus 1 right parenthesis to the power of text th end text end exponent comma left parenthesis n plus 1 right parenthesis to the power of text th end text end exponent text and end text left parenthesis r plus 1 right parenthesis to the power of text th end text end exponent text terms of an AP are in GP end text$ and m, n, r are in HP, then the value of the ratio of the common difference to the first term of the AP is

$text If the end text left parenthesis m plus 1 right parenthesis to the power of text th end text end exponent comma left parenthesis n plus 1 right parenthesis to the power of text th end text end exponent text and end text left parenthesis r plus 1 right parenthesis to the power of text th end text end exponent text terms of an AP are in GP end text$ and m, n, r are in HP, then the value of the ratio of the common difference to the first term of the AP is

parallel

If the harmonic mean between a and b is H, then $fraction numerator H plus a over denominator H minus a end fraction plus fraction numerator H plus b over denominator H minus b end fraction equals$

If the harmonic mean between a and b is H, then $fraction numerator H plus a over denominator H minus a end fraction plus fraction numerator H plus b over denominator H minus b end fraction equals$

If $fraction numerator a to the power of n plus 1 end exponent plus b to the power of n plus 1 end exponent over denominator a to the power of n end exponent plus b to the power of n end exponent end fraction$ is the harmonic mean between $a$ and $b$ , then the value of $n$ is

If $fraction numerator a to the power of n plus 1 end exponent plus b to the power of n plus 1 end exponent over denominator a to the power of n end exponent plus b to the power of n end exponent end fraction$ is the harmonic mean between $a$ and $b$ , then the value of $n$ is

If a ,b, c are three distinct positive real numbers which are in $text HP, then end text fraction numerator 3 a plus 2 b over denominator 2 a minus b end fraction plus fraction numerator 3 c plus 2 b over denominator 2 c minus b end fraction text is end text$

If a ,b, c are three distinct positive real numbers which are in $text HP, then end text fraction numerator 3 a plus 2 b over denominator 2 a minus b end fraction plus fraction numerator 3 c plus 2 b over denominator 2 c minus b end fraction text is end text$

parallel

If the $m to the power of text th end text end exponent$ term of an $H P$ is $n$ and $n to the power of text th end text end exponent$ is $m$ , then the $r to the power of text th end text end exponent$ term will be

If the $m to the power of text th end text end exponent$ term of an $H P$ is $n$ and $n to the power of text th end text end exponent$ is $m$ , then the $r to the power of text th end text end exponent$ term will be

If $left parenthesis a plus 2 b plus 2 c right parenthesis left parenthesis a minus 2 b plus 2 c right parenthesis equals a to the power of 2 end exponent plus 4 c to the power of 2 end exponent text , end text$ where a ,b, c are nonzero numbers. Then a ,b,c are in

If $left parenthesis a plus 2 b plus 2 c right parenthesis left parenthesis a minus 2 b plus 2 c right parenthesis equals a to the power of 2 end exponent plus 4 c to the power of 2 end exponent text , end text$ where a ,b, c are nonzero numbers. Then a ,b,c are in

The sum of infinite terms of a GP is x and on squaring the each term of it, the sum will be y. Then the common ratio of this series is

The sum of infinite terms of a GP is x and on squaring the each term of it, the sum will be y. Then the common ratio of this series is

parallel

Alcohols are ,acidic in nature because hydrogen is attached to oxygen which is an electronegative element. Alcohol is weaker acid than water because $O H to the power of minus end exponent$ ion is more stable than $R minus O to the power of minus end exponent$ ion $R minus 0 to the power of minus end exponent$ is less stable, due to +I effect of the alkyl group., Acidity of alcohols increases with increase:' in ' the stability of acid anion.

Some alcohols . like $C H subscript 3 end subscript minus O H comma C F subscript 3 end subscript minus C H subscript 2 end subscript minus O H$ , $blank open parentheses C F subscript 3 end subscript close parentheses subscript 3 end subscript C minus O H$
are more acidic than water:
The strongest conjugate base out of the following is :

Alcohols are ,acidic in nature because hydrogen is attached to oxygen which is an electronegative element. Alcohol is weaker acid than water because $O H to the power of minus end exponent$ ion is more stable than $R minus O to the power of minus end exponent$ ion $R minus 0 to the power of minus end exponent$ is less stable, due to +I effect of the alkyl group., Acidity of alcohols increases with increase:' in ' the stability of acid anion.

Some alcohols . like $C H subscript 3 end subscript minus O H comma C F subscript 3 end subscript minus C H subscript 2 end subscript minus O H$ , $blank open parentheses C F subscript 3 end subscript close parentheses subscript 3 end subscript C minus O H$
are more acidic than water:
The strongest conjugate base out of the following is :

Chemistry-General

Final product (D) in the sequence of reactions is:

Final product (D) in the sequence of reactions is:

Chemistry-General

How many isomers of C₅H₁₁OH will be primary alcohols?

How many isomers of C₅H₁₁OH will be primary alcohols?

Chemistry-General

parallel

The number of solutions the equation $x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x plus 2 c o s invisible function application x equals 0 text in end text left square bracket 0 , 2 pi right square bracket$ is

The number of solutions the equation $x to the power of 3 end exponent plus 2 x to the power of 2 end exponent plus 5 x plus 2 c o s invisible function application x equals 0 text in end text left square bracket 0 , 2 pi right square bracket$ is

$text If end text theta element of left square bracket 0 , 5 pi right square bracket text and end text r element of R text such that end text 2 s i n invisible function application theta equals r to the power of 4 end exponent minus 2 r to the power of 2 end exponent plus 3$ then the maximum number of values of the pair $left parenthesis r comma theta right parenthesis$ is

$text If end text theta element of left square bracket 0 , 5 pi right square bracket text and end text r element of R text such that end text 2 s i n invisible function application theta equals r to the power of 4 end exponent minus 2 r to the power of 2 end exponent plus 3$ then the maximum number of values of the pair $left parenthesis r comma theta right parenthesis$ is

Which of the following will be the major product when

is treated with dil. H₂SO₄ in the presence of HgSO₄ ?

Which of the following will be the major product when

is treated with dil. H₂SO₄ in the presence of HgSO₄ ?

Chemistry-General

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.