# Find $x$ such that the sequence $\sin\left(\left(1+\frac1{n}\right)^x\right)$ converges pointwise

Find a set on which the sequence $\sin\left(\left(1+\frac1{n}\right)^x\right)$ converge pointwise. Thanks for any help.

I think we are required to find for which values of $x$ does the sequence converge pointwise!

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Try showing us where you got stuck, this way you learn way more then that we just give you the answer. – sxd Jan 7 '12 at 2:02
Notice that sin is continuous everywhere; so if $\left( 1 + \frac1n \right)^x$ converges, then the given sequence also would converge. Does this hint help? – Srivatsan Jan 7 '12 at 2:02
yes it helps, thanks – neemy Jan 7 '12 at 2:22

This is not as interesting as $\sin ((1+x)^n)$ would be...
Since $(1+1/n)\to 1$, we have $(1+1/n)^x\to 1^x=1$ regardless of the value of $x$. So the limit is $\sin 1$ for all $x$.