Question

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 1

Ans: (A)
\(: t_{r}=(2 r-1)^{3}\)
$$
S_{n}=\sum_{r=1}^{n} t_{r}=8 \sum_{r=1}^{n} r^{3}-12 \sum_{r=1}^{n} r^{2}+6 \sum_{r=1}^{n} r-\sum_{r=1}^{n} 1=n^{2}\left(2 n^{2}-1\right)
$$

Answer 2

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Answer 3

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