Question

Find the sum of n terms of the series root2, root8, root18 ,root32...is


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Answer 1

The series can be rewritten as sqrt(2) + 2*sqrt(2) + 3*sqrt(2) + 4*sqrt(2) + .....

So the nth sum S(n) = sqrt(2) * (1 + 2 + 3 + ..... + n) = sqrt(2) * n*(n+1)/2.