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The sum of 24 terms of the following ser...

The sum of 24 terms of the following series `sqrt(2)+sqrt(8)+sqrt(18)+sqrt(32)+......` is

A

300

B

`200sqrt(2)`

C

`300sqrt(2)`

D

`250sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
c
` sqrt(2) +sqrt(8) +sqrt(18) +sqrt(32) +...`
` = 1 xx sqrt(2) +2sqrt(2) +3sqrt(2) +4sqrt(2)+...`
` = sqrt(2) (1+2+3+4 + ..."upto 24 terms")`
` sqrt(2) xx (24 xx25)/2 = 300sqrt(2)" " [ :' Sigma n = (n(n+1))/2]`
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