(C) Given,$S_n = \sum_{k=1}^{n} k^3$ and $T_n = \sum_{k=1}^{n} k$.We know that the sum of the first $n$ natural numbers is $T_n = \frac{n(n+1)}{2}$.Th

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(C) Given,$S_n = \sum_{k=1}^{n} k^3$ and $T_n = \sum_{k=1}^{n} k$.We know that the sum of the first $n$ natural numbers is $T_n = \frac{n(n+1)}{2}$.The sum of the cubes of the first $n$ natural numbers is $S_n = \left[\frac{n(n+1)}{2}\right]^2$.Substituting $T_n$ into the expression for $S_n$,we get $S_n = (T_n)^2$.Therefore,the correct relation is $S_n = T_n^2$.

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

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If $S_n = 1^3 + 2^3 + \ldots + n^3$ and $T_n = 1 + 2 + \ldots + n$,then

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A
$S_n = T_{n^3}$
B
$S_n = T_{n^2}$
C
$S_n = T_n^2$
D
$S_n = T_n^3$

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

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DifficultJEE MAIN 2023

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MediumKCET 2010

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If $S_n = 1^3 + 2^3 + \ldots + n^3$ and $T_n = 1 + 2 + \ldots + n$,then

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