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Infinite series convergence I

cacophony

New member
Apr 17, 2013
4
Test these for convergence.

1.
infinity
E.......n!/(n! + 3^n)
n = 0

2.
infinity
E.......(n - (1/n))^-n
n = 1

Btw, E means sum.

Which tests should I use to solve these?
 
Last edited by a moderator:

chisigma

Well-known member
Feb 13, 2012
1,704
1. $\displaystyle \sum_{n=0}^{\infty} \frac{n!}{n! + 3^n}$
What is $\displaystyle \lim_{n \rightarrow \infty} \frac{n!}{n! + 3^n}$?...

Kind regards

$\chi$ $\sigma$
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667