WBJEE · Maths · Sequences and Series
The sum of \(n\) terms of the following series \(1^{3}+3^{3}+5^{3}+7^{3}+\ldots\) is
- A \(n^{2}\left(2 n^{2}-1\right)\)
- B \(n^{3}(n-1)\)
- C \(n^{3}+8 n+4\)
- D \(2 n^{4}+3 n^{2}\)
Answer & Solution
Correct Answer
(A) \(n^{2}\left(2 n^{2}-1\right)\)
Step-by-step Solution
Detailed explanation
We have. \(\mathrm{1}^{3}+3^{3}+5^{3}+7^{3}+\ldots\) \(\begin{aligned} \text { Now, } T_{n} &=(2 n-1)^{3} \\ &=8 n^{3}-3(2 n)^{2}(1)+3(2 n)\left(0^{2}-(\pi)^{3}\right.\\ &=8 n^{3}-12 n^{2}+6 n-1 \end{aligned}\) \(\therefore \quad S_{n}=\Sigma T_{n}\)…
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