1.

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»

Correct option is (C) \(2n^2(n+1)^2\)

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

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

\(=\sum(2n)^3\) \(=\sum8n^3\)

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

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

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

Correct option is C) 2n2 (n + 1)2 



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