(C) The formula for the sum of the cubes of the first $n$ natural numbers is given by:$S_n = \left[ \frac{n(n+1)}{2} \right]^2$Here,$n = 15$.Substitut

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(C) The formula for the sum of the cubes of the first $n$ natural numbers is given by:$S_n = \left[ \frac{n(n+1)}{2} \right]^2$Here,$n = 15$.Substituting the value of $n$ into the formula:$S_{15} = \left[ \frac{15(15+1)}{2} \right]^2$$S_{15} = \left[ \frac{15 \times 16}{2} \right]^2$$S_{15} = (15 \times 8)^2$$S_{15} = (120)^2$$S_{15} = 14400$.

Competitive Quantitative Aptitude Progression and Sequence Progression and Sequence

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The sum of $1^3 + 2^3 + 3^3 + 4^3 + ..... + 15^3$ is:

A
$22000$
B
$10000$
C
$14400$
D
$15000$

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Progression and Sequence

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Progression and Sequence

The sum of the series $\frac{1}{{1 + {1^2} + {1^4}}} + \frac{2}{{1 + {2^2} + {2^4}}} + \frac{3}{{1 + {3^2} + {3^4}}} + \dots$ to $n$ terms is

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If $s$ is the sum of an infinite $G.P.$ and $a$ is the first term,then the common ratio $r$ is given by:

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The sum of $n$ terms of the series whose $n^{th}$ term is $n(n + 1)$ is equal to

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The sum of all two-digit numbers which,when divided by $4$,yield unity as a remainder is:

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If the sum of the first $n$ terms of two arithmetic progressions $3, 7, 11, 15, \ldots$ and $30, 33, 36, 39, \ldots$ are equal,then find the value of $n$.

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The sum of $1^3 + 2^3 + 3^3 + 4^3 + ..... + 15^3$ is:

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The sum of the series $\frac{1}{{1 + {1^2} + {1^4}}} + \frac{2}{{1 + {2^2} + {2^4}}} + \frac{3}{{1 + {3^2} + {3^4}}} + \dots$ to $n$ terms is

If $s$ is the sum of an infinite $G.P.$ and $a$ is the first term,then the common ratio $r$ is given by:

The sum of $n$ terms of the series whose $n^{th}$ term is $n(n + 1)$ is equal to

The sum of all two-digit numbers which,when divided by $4$,yield unity as a remainder is:

If the sum of the first $n$ terms of two arithmetic progressions $3, 7, 11, 15, \ldots$ and $30, 33, 36, 39, \ldots$ are equal,then find the value of $n$.

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