Go Back   TestMagic Forums > Test preparation > GRE Subject Tests > GRE Subject Test: Mathematics
Register Forum Rules FAQ Members List Calendar Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old 2008 March 21st, 05:07 AM   #1 (permalink)
I JUST got here.
 
Join Date: Mar 2008
Posts: 2
Eschewy just joined TestMagic.
Problem 37 on the Practice Test - I need help.

I need some quick help with problem 37 from the practice test:

What is the sum of k^2/k! for k= 0 -> infinity?

The booklet claims that the answer is 2*e, and I know for a fact that the sum of 1/k! is e, but I don't see how to get from one to the other. Any help would be greatly appreciated.
Eschewy is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Old 2008 March 21st, 07:28 AM   #2 (permalink)
I JUST got here.
 
Join Date: Mar 2008
Posts: 2
Eschewy just joined TestMagic.
False alarm guys - I found the answer elsewhere on another message board.

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.
Eschewy is offline  
Digg this Post!Add Post to del.icio.usBookmark Post in TechnoratiFurl this Post!Google Bookmark this Post!Reddit!
Reply With Quote
Reply


Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

What you can do
You cannot post new threads
You cannot post replies
You cannot post attachments
You cannot edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


All times are GMT. The time now is 01:52 AM.

Contact TestMagic   TestMagic Forums      Archive   Privacy Statement

TestMagic Locations   Legal   Privacy


SEO by vBSEO 3.2.0
Copyright © 2009 TestMagic
Ad Management by RedTyger

Scroll Up