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Math helps please

The questions asks to show that summation n=1 to infinity x^n / n! converges for all x and deduce that the limit of x^n / n! = 0 for all x.

I assumed that we were supposed to find the radius of convergence/ interval of convergence to prove all these x's to be convergent. But when I did, the radius = infinity.

So what does it mean when the radius of convergence = infinity? Does it mean all x's are convergent?

Also, how do I deduce the second part of this problem? squeeze theorem? SOMETHING? D:

February 19, 2013

5 Comments • Newest first

Blackyoshi

I'm scared of continuing my calculus class now...

Reply February 19, 2013
cchpm

[quote=Reticent]oh, thanks! and could you explain what happens if the radius of convergence goes to infinity for future reference. :x
WHAT A MINUTE. Doing the ratio test doesn't prove the "limit n-> infinity x^n / n! goes to 0" though. :C[/quote]

if you get infinity when do ratio test, then the series is divergent.

Reply February 19, 2013 - edited
Reticent

[quote=VitaminEliza]use the ratio test: an+1/an
lim n->infinity x^n+1/(n+1)n! x n!/x^n
cancel out the n's and you get
lim n->infinity x/(n+1) = 0
it will converge for any value of x since denominator has n[/quote]

oh, thanks! and could you explain what happens if the radius of convergence goes to infinity for future reference. :x
WHAT A MINUTE. Doing the ratio test doesn't prove the "limit n-> infinity x^n / n! goes to 0" though. :C

Reply February 19, 2013 - edited
cchpm

Glad I have my calc book nearby ... lets see ... chapter 8, series. ...

EDIT: yea, as the guy below me says, you use ratio test. and a small tip, you usually use ratio test every time you see factorial.

Reply February 19, 2013 - edited
ZOMGitjon

"-insert teacher's name- IS AWESOME!"

how i get points

Reply February 19, 2013 - edited