Question

limit n tends to infinity (1+x)(1+X^2)(1+^x3)..........(1+x^2n)=????

Answer 1

is that \(x^3\) or \(x^4\) ? it should be\[(1+x)(1+x^2)(1+x^4)..........(1+x^{2n})\]

Answer 2

anyway

Hint :

multiply and divide by \(1-x\) \[\frac{\color\red{(1-x)(1+x)}(1+x^2)(1+x^4)...(1+x^{2n})}{1-x}\]\[\frac{\color\red{(1-x^2)}\color\green{(1+x^2)}(1+x^4)...(1+x^{2n})}{1-x}\]\[\frac{\color\green{(1-x^4)}(1+x^4)...(1+x^{2n})}{1-x}\]...

Answer 3

and do the limit for 2 cases

1...\(|x|<1\)

2...\(|x|\ge1\)