9768 #37

Forum for the GRE subject test in mathematics.
YKM
Posts: 45
Joined: Mon Aug 08, 2011 10:25 am

9768 #37

Postby YKM » Mon Aug 08, 2011 10:47 am

Dear all,

Can anyone give me some idea on the infinite serious below?

{K=1 to infinity}, (K^2) / K! = ??

Thanks

hadimotamedi
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

Re: 9768 #37

Postby hadimotamedi » Tue Aug 09, 2011 12:16 am

Please note that the guys have previously answered it, as the following :
"
First note that, for k >= 1, k^2/k! = k/(k-1)!. By a change of
variable we may write sum(k=1 to oo) k/(k-1)! = sum(k=0 to oo) (k+1)/
k! = sum(k=0 to oo) 1/k! + sum(k=0 to oo) k/k!. The first term is e.
For the second term note that for the case k=0 the summand is zero, so
we can write this as sum(k=1 to oo) k/k! = sum(k=1 to oo) 1/(k-1)! =
sum(k=0 to oo) 1/k!, where the last equality follows from another
change of variable. So this term is also e."

YKM
Posts: 45
Joined: Mon Aug 08, 2011 10:25 am

Re: 9768 #37

Postby YKM » Tue Aug 09, 2011 10:32 am

thanks, got it !! :o




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