Question

The sum to $n$ terms of the series $1^3+3^3+5^3+\dots$ is

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

Answer 1

Answer: (B)

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

$\sum {(2r-1)}^3=8\sum r^3-\sum 1-12\sum r^2+6\sum r\sum {(2r-1)}^3=2n^2\times (n+1{)}^2-n-2n(n+1)(2n+1)+3n(n+1)\sum {(2r-1)}^3=n^2(2n^2-1)$