Uniform Convergence... What did I wrong for this function?

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I want to know if this function is unif.conv. or not...

Actually it is one of the my mid-exem problems.

I got zero score for it....

What did I wrong in this problem?

and What is the easiest way to see whether it is unif.conv. or not?

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Evaluate $|f_n(x)-f(x)|$ at $x_n:=1-1/n$. You should get $|1+(1-1/n)^n-(1-1/n)^2|$. This has limit $e^{-1}\neq0$.