Maths-
General
Easy
Question
The sum of the series
upto 20 terms is
- 188090
- 189080
- 199080
- 199089
The correct answer is: 188090
Here, ![T subscript n end subscript o f blank t h e A P blank 12 comma 3 horizontal ellipsis equals n](data:image/png;base64,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)
and
of the AP ![35 comma 7 horizontal ellipsis equals 2 n plus 1](data:image/png;base64,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)
of given series![equals n open parentheses 2 n plus 1 close parentheses to the power of 2 end exponent equals 4 n to the power of 3 end exponent plus 4 n to the power of 2 end exponent plus n](data:image/png;base64,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)
Hence, ![S equals not stretchy sum subscript n equals 1 end subscript superscript 20 end superscript T subscript n end subscript equals 4 not stretchy sum subscript n equals 1 end subscript superscript 20 end superscript n to the power of 3 end exponent plus 4 not stretchy sum subscript n equals 1 end subscript superscript 20 end superscript n to the power of 2 end exponent plus not stretchy sum subscript n equals 1 end subscript superscript 20 end superscript n](data:image/png;base64,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)
+![fraction numerator 1 over denominator 2 end fraction 20.21](data:image/png;base64,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)
![equals 188090](data:image/png;base64,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)
Related Questions to study
maths-
The sum of
terms of the series
will be
The sum of
terms of the series
will be
maths-General
maths-
Orthocentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is
Orthocentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is
maths-General
maths-
The line
and
intersect the line
at P and Q respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R
Statement - 1 : The ratio PR : RQ equals ![2 square root of 2 colon square root of 5](data:image/png;base64,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)
Statement - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.
The line
and
intersect the line
at P and Q respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R
Statement - 1 : The ratio PR : RQ equals ![2 square root of 2 colon square root of 5](data:image/png;base64,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)
Statement - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.
maths-General
maths-
If one of the lines given by
is 3x + 4y = 0, then c equals :
If one of the lines given by
is 3x + 4y = 0, then c equals :
maths-General
maths-
If the sum of first
natural numbers is 1/5 times the sum of their squares, then the value of
is
If the sum of first
natural numbers is 1/5 times the sum of their squares, then the value of
is
maths-General
maths-
If
, then the value of x in terms of y is
If
, then the value of x in terms of y is
maths-General
maths-
Given the lines y + 2x = 3 and y + 2x = 5 cut the axes at A, B and C, D respectively.
Statement- I ABDC forms quadrilateral and point (2, 3) lies inside the quadrilateral
Statement- II Point lies on same side of the lines.
Given the lines y + 2x = 3 and y + 2x = 5 cut the axes at A, B and C, D respectively.
Statement- I ABDC forms quadrilateral and point (2, 3) lies inside the quadrilateral
Statement- II Point lies on same side of the lines.
maths-General
Maths-
The x-coordinates of the vertices of a square of unit area are the roots of the equation
and the y-coordinates of the vertices are the roots of the equation
then the possible vertices of the square is/are :
therefore the possible vertices of the square are (1,1),(1,2),(2,1),(2,2) and (−1,1),(−1,2),(−2,2),(−2,1)
The x-coordinates of the vertices of a square of unit area are the roots of the equation
and the y-coordinates of the vertices are the roots of the equation
then the possible vertices of the square is/are :
Maths-General
therefore the possible vertices of the square are (1,1),(1,2),(2,1),(2,2) and (−1,1),(−1,2),(−2,2),(−2,1)
Maths-
The straight lines x + y = 0, 3x + y - 4 = 0 and x + 3y -4 = 0 form a triangle which is
therefore it forms an isosceles triangle
The straight lines x + y = 0, 3x + y - 4 = 0 and x + 3y -4 = 0 form a triangle which is
Maths-General
therefore it forms an isosceles triangle
Maths-
Equation of a straight line passing through the point (4, 5) and equally inclined to the lines 3x = 4y + 7 and 5y = 12x + 6 is
Equation of a straight line passing through the point (4, 5) and equally inclined to the lines 3x = 4y + 7 and 5y = 12x + 6 is
Maths-General
Maths-
If the equation
represents a pair of lines whose slopes are m and
, then value(s) of a is/are -
If the equation
represents a pair of lines whose slopes are m and
, then value(s) of a is/are -
Maths-General
maths-
The curve passing through the points of intersection of
and
represents a pair of straight lines which are
The curve passing through the points of intersection of
and
represents a pair of straight lines which are
maths-General
maths-
The number of divisors of
and
are in
The number of divisors of
and
are in
maths-General
maths-
The equation of perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0) is -
The equation of perpendicular bisector of the line segment joining the points (1, 2) and (–2, 0) is -
maths-General
maths-
If
are in
If
are in
maths-General