Question

Sum to ‘n’ terms of 2³ + 4³ + 6³ + ……………. is 

A) 4n² (n + 1)² 

B) 4n² (n – 1)² 

C) 2n² (n + 1)² 

D) n² (n + 1)²

Answer 1

Correct option is (C) \(2n^2(n+1)^2\)

\(S_n=2^3+4^3+6^3+.......+\) upto n terms

\(=2^3+4^3+6^3+.......+(2n)^3\)

\(=\sum(2n)^3\) \(=\sum8n^3\)

\(=8\sum n^3\) \(=8\left(\frac{n(n+1)}2\right)^2\)

\(=\frac{8n^2(n+1)^2}4\)

\(=2n^2(n+1)^2\)

Answer 2

Correct option is C) 2n² (n + 1)²