AP EAMCET · Maths · Sequences and Series
If \(S_n=1^3+2^3+\ldots+n^3\) and \(T_n=1+2+\ldots+n\), then
- A \(S_n=T_{n^3}\)
- B \(S_n=T_{n^2}\)
- C \(S_n=T_n^2\)
- D \(S_n=T_n^3\)
Answer & Solution
Correct Answer
(C) \(S_n=T_n^2\)
Step-by-step Solution
Detailed explanation
Given, \(S_n=1^3+2^3+\ldots+n^3=\Sigma n^3\) \(\begin{array}{rlrl} & \text { and } & T_n & =1+2+\ldots+n=\Sigma n \\ & & S_n & =\Sigma n^3=\left[\frac{n(n+1)}{2}\right]^2 \\ & & =\{\Sigma(n)\}^2=T_n^2 \\ & \therefore & S_n & =T_n^2\end{array}\)
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