# Thread: 3 fun problems on analysis

1. ## 3 fun problems on analysis

1. Is the series Sigma $(-1)^n * (n!)^2/((2n)!)$ convergent

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

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

Thx guys!

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

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

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

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

Bobak

3. 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?

4. $\frac{\frac{(n+1)!(n+1)!}{(2n+2)!}}{\frac{(n)!(n)! }{(2n)!}} = \frac{(n+1)^2}{(2n+2)(2n+1)}$

can you finish off?

Bobak

5. 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