Find the sum

Algebra Level 2

Find the sum of n n terms of the series.
2 + 8 + 18 + 32 + ⋯ \sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32}+ \cdots

2 × n ( n + 1 ) 2 \frac {\sqrt{2} × n(n+1)}{2} 2n(n+1) n ( n + 1 ) 2 \frac {n(n+1)}{2} n × 2 \sqrt{2}

Sonveer Yadav by Sonveer Yadav , 22, India

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1 solution

Akshat Sharda
Mar 15, 2016

2 + 2 2 + 3 2 + 4 2 + … 2 ( 1 + 2 + 3 + 4 + … + n ) 2 ⋅ n ( n + 1 ) 2 \sqrt{2}+2\sqrt{2}+3\sqrt{2}+4\sqrt{2}+\ldots \\ \sqrt{2}(1+2+3+4+\ldots+n) \\ \sqrt{2} \cdot \frac{n(n+1)}{2}

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