- #1

jnimagine

- 178

- 0

**series; convergence, divergence...**

## Homework Statement

1. sum(infinity,n=1) n!/1.3.5...(2n-1)

2. sum(infinity, n=1) (-1)^n arcsin(-1/n)

3. sum(infinity, n=0) arcsin(1/n^2) / arctan(1/n^2)

## The Attempt at a Solution

1. i used the ratio test and then i ended up with lim((n+1)(2n-1)/2n+1)) and when i solve the limit i get infinity...

but it's supposed to be convergent... so I'm obviously doing something wrong... :(

2. by alternating series test, it converges

but it's suppsoed to be conditionally convergent, so i tried using the limit test...

how do you approch this problem?? I tried using l'hospital's rule and stuff... but i ended

up with a mess lol

3. in general, when there's inverse trig functions how do u work it out?