# 3 fun problems on analysis

• Apr 2nd 2009, 02:40 AM
luoginator
3 fun problems on analysis
1. Is the series Sigma $\displaystyle (-1)^n * (n!)^2/((2n)!)$ convergent

2. Determine the radius of convergence of the power series Sigma
$\displaystyle (-1)^n * ((n+3)/(3^n+4^n)) * x^(3n)$

3. Is the series Sigma$\displaystyle n!/(n^n)$convergent

Thx guys!
• Apr 2nd 2009, 03:15 AM
bobak
Quote:

Originally Posted by luoginator
1. Is the series Sigma $\displaystyle (-1)^n * (n!)^2/((2n)!)$ convergent

2. Determine the radius of convergence of the power series Sigma
$\displaystyle (-1)^n * ((n+3)/(3^n+4^n)) * x^(3n)$

3. Is the series Sigma$\displaystyle n!/(n^n)$convergent

Thx guys!

alternating series test/ ratio test can solve all of these, what have you tried ?

Bobak
• Apr 2nd 2009, 03:34 AM
luoginator
umm..ive tried ratio test...but it doesn't seem to be workin properly coz the fraction is sooooooo huge lol....any good idea man:)?
• Apr 2nd 2009, 04:07 AM
bobak
$\displaystyle \frac{\frac{(n+1)!(n+1)!}{(2n+2)!}}{\frac{(n)!(n)! }{(2n)!}} = \frac{(n+1)^2}{(2n+2)(2n+1)}$

can you finish off?

Bobak
• Apr 2nd 2009, 04:09 AM
luoginator
actually..im worried about 2 and 3....i actually used lim test...like lim ak =0 to test its convergency for question 1....but ur way is nice anyway:)