Question

For all even integral values of n , lim
x-infinite (X+1)^-n exists

Answer 1

In general the limit does not exist.

Case:1 If $n>0$ .

In this case, $\lim_{x\to \infty}(x+1)^{-n}=\lim_{x\to \infty} \frac{1}{(x+1)^n}$ $=0$

Hence the limit exists.

Case: 2 If $n=0$

In this case, $\lim_{x\to \infty}{(x+1)^{-n}}=1$

Hence the limit exists.

Case:3 If $n<0$

In this case, $\lim_{x\to \infty}(x+1)^{-n}=\infty$

And the limit does not exist.