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If x= (1)/(sqrt2) + (1)/(2) + (1)/(2sqr...

If `x= (1)/(sqrt2) + (1)/(2) + (1)/(2sqrt2) +… + oo`, then find the value of `x + (1)/(x)`.

A

`sqrt2`

B

`2sqrt2`

C

`3sqrt2`

D

`4sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
`x = (1)/(sqrt2) + (1)/(2) + (1)/(2sqrt2)+ ... oo`
`x =((1)/(sqrt2))/(1-(1)/(sqrt2))= (1)/(sqrt2 -1)`
`x = (1)/(sqrt2 -1) = sqrt2 + 1 rArr (1)/(x) = sqrt2 -1`
`therefore x + (1)/(x)= sqrt2 + 1+ sqrt2 -1 = 2sqrt2`.
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