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hello all

how would one prove that [tex]\lim_{n\rightarrow\infty}\frac{x^{n+1}}{(n+1)!}=0[/tex] [tex]\forall x\in\Re [/tex] now when i try to plot it on mathematica for x=200, on the plot it displays that [tex]200^{n+1}>(n+1)![/tex] how could it possibly converge for any value of x? the reason why i need to prove this is because im trying to show that a function is analytic, would somebody have an anology or a graphical explaination of what is meant by an analytic function?

Steven

how would one prove that [tex]\lim_{n\rightarrow\infty}\frac{x^{n+1}}{(n+1)!}=0[/tex] [tex]\forall x\in\Re [/tex] now when i try to plot it on mathematica for x=200, on the plot it displays that [tex]200^{n+1}>(n+1)![/tex] how could it possibly converge for any value of x? the reason why i need to prove this is because im trying to show that a function is analytic, would somebody have an anology or a graphical explaination of what is meant by an analytic function?

Steven

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