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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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