Sunday, 13 August 2017

convergence divergence - Prove that xn/n! converges to 0 for all x

Prove that an=xn/n!0 for all x



Here is what I tried, but it seems to lead to nowhere.



Choose ϵ>0. We need to show that there exists NN such that for all n>N we have |an|<ϵ



So, |(xn/n!)|<ϵ|xn|<n!ϵ (since n! is positive we ignore the absolute signs). So |x|/(ϵ1/n)<[n!(1/n)].
Now I am stuck in solving this for n, and hence finding N ...

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