(C) The sum of the cubes of the first $n$ natural numbers is given by the formula: $S_n = \left[ \frac{n(n+1)}{2} \right]^2 = \frac{n^2(n+1)^2}{4}$ He

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(C) The sum of the cubes of the first $n$ natural numbers is given by the formula: $S_n = \left[ \frac{n(n+1)}{2} \right]^2 = \frac{n^2(n+1)^2}{4}$ Here,$n = 15$. Substituting the value of $n$: $S_{15} = \frac{15^2 \times (15+1)^2}{4} = \frac{225 \times 16^2}{4} = \frac{225 \times 256}{4} = 225 \times 64 = 14400$.

Class 11 Mathematics Sequences and Series nth term of special series, Sum to n terms and Infinite number of terms

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The sum of $1^3 + 2^3 + 3^3 + 4^3 + \dots + 15^3$ is

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

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Class 11

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Sequences and Series

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nth term of special series, Sum to n terms and Infinite number of terms

$1^2+\left(1^2+2^2\right)+\left(1^2+2^2+3^2\right)+\ldots+\left(1^2+2^2+\ldots+n^2\right)=$

EasyAP EAMCET 2019

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Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = n(n+2)$.

Easy

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The first term of the ${11^{th}}$ group in the following sequence of groups $(1), (2, 3, 4), (5, 6, 7, 8, 9), \dots$ is

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The mean of the squares of the first $n$ natural numbers is

EasyAP EAMCET 2021

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The sum of an infinite number of terms in a $G.P.$ is $20$ and the sum of their squares is $100$. The common ratio of the $G.P.$ is:

MediumAIEEE 2002

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The sum of $1^3 + 2^3 + 3^3 + 4^3 + \dots + 15^3$ is

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