lim(n to oo) (1+x)(1+x^(2))(1+x^(4))…………...

`lim_(n to oo) (1+x)(1+x^(2))(1+x^(4))……………(1+x^(2n)),|x|lt1` is

`(1)/(x-1)`

`(1)/(1-x)`

`1-x`

`x-1`

Text Solution

Verified by Experts

The correct Answer is:

We have ,
`lim_(xto oo) {(1+x)(1+x^2)(1+x^4)......(1+x^(2n))}`
`lim_(xto oo) {((1-x)(1+x)(1+x^2)......(1+x^(2n)))/(1-x)}`
` =lim_(nto oo) (1-x^(4n))/(1-x)`
` =(1-0)/(1-x)=(1)/(1-x)" "[because lim_(xto oo) x^4n=0 " for" -1 lt x lt 1]`

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