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If x=1+1/(3+1/(3+1/(2...oo))) then the v...

If `x=1+1/(3+1/(3+1/(2...oo)))` then the value of x is

A

`sqrt(5/2)`

B

`sqrt(3/2)`

C

`sqrt(7/3)`

D

`sqrt(5/3)`

Text Solution

Verified by Experts

The correct Answer is:
4
`x = 1 + (1)/(3+(1)/(2+(1)/(3+1/(2...oo))))`
`= 1 + (1)/(3+(1)/(1 + x))`
`= 1 + (1 + x)/(4 + 3x)`
or `3x^(2) = 5`
or `x = sqrt(5/3)` (as x is positive)
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