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What is the sum of n terms of the series...

What is the sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+..`

A

`(n(n-1))/(sqrt(2))`

B

`sqrt(2n)(n+1)`

C

`(n(n+1))/(sqrt(2))`

D

`(n(n-1))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`sqrt(2)+sqrt(8)+sqrt(18)+sqrt(32)+......`
`=sqrt(2)+2sqrt(2)+3sqrt(2)+4sqrt(2)+......`
`:." "S_(n)=sqrt(2)[1+2+3+4+...."n terms"]`
`=sqrt(2)(n(n+1))/(2)=(n(n+1))/(sqrt(2))`
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