Question

The sum of n terms of the following series; $1^3 + 3^3 + 5^3 + 7^3 + ....$ is

• A. $n^2(2n^2 - 1)$
• B. $n^3(n - 1)$
• C. $n^3 + 8n + 4$
• D. $2n^4 + 3n^2$

Answer 1

Answer: (A)

$n^2(2n^2 - 1)$

Answer 2

$t_{r}=\left(2r-1\right)^{3}$
$S_n \displaystyle \sum_{r=1}^nt_r=8\displaystyle \sum_{r=1}^nr^3-12\displaystyle \sum_{r=1}^nr^2-6\displaystyle \sum_{r=1}^nr-\displaystyle \sum_{r=1}^n1=n^2(2n^2-1)$