If x1=3a n dx(n+1)=sqrt(2+xn),ngeq1,t h ...

If `x_1=3a n dx_(n+1)=sqrt(2+x_n),ngeq1,t h e n""("lim")_(xvecoo)x_n` is `-1` (b) `2` (c) `sqrt(5)` (d) 3

A

0

B

`(1)/(2)`

C

log2

D

`e^(4)`

Text Solution

Verified by Experts

The correct Answer is:

B

`x_(n+1)=sqrt(2+x_(n))`
or `underset(ntooo)limx_(n+1)=sqrt(2+underset(ntooo)limx_(n))`
or `t=sqrt(2+t)" "(becauseunderset(xtooo)limx_(n+1)=underset(xtooo)limx_(n)=t)`
or `t^(2)-t-2=0`
or`(t-2)(t+1)=0`
or `t=2" "(becausex_(n)gt0AAn,tgt0)`

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