Sum of n terms of the series √2 + √8 + √18 + √32 + ...... is ​ A. B. 2n (n+1) ​A. n(n+1)/2 B. 2n(n+1)

Question

Sum of n terms of the series √2 + √8 + √18 + √32 + ...... is

A. \(\frac{n(n+1)}{2}\)

B. 2n (n+1)

C. \(\frac{n(n+1)}{\sqrt2}\)

D. 1

Answer 1

 The given A.P is √2 + √8 + √18 + √32 +....

The simplified A.P.  is 

√2,2√2,3√2,4√2, .......

Here a = √2

d = 2√2 - √2 = √2

S_n = \(\frac{n}{2}\)(2a + (n–1) d) 

= \(\frac{n}{2}\)(2√2 + (n–1)√2) 

= √2n/2 (1 + n) 

= n (n + 1)/√2