Series help: Sum of 1/sqrt(n^3+1) with n = 1 to infinity

[paulxzt]

Determine whether the series is convergent of divergent.

1) Sum of 1/sqrt(n^3+1) with n = 1 to infinity.

I rewrote it as (n^3+1)^-1/2 and divided the n^3 inside and got ( 1 + 1/n^3) ^-.5 and took the limit as n->infinity = 1?

i think i did it really wrong, any help? thanks

and 2) Use the comparison test to determine whether the series is convergent or divergent: sum of sqrt(n) / ( n-1) with n = 2 to infinity.

thanks for any help..

 

[skeeter]

1. limit comparison test with the known convergent p-series 1/n^3/2.

2. direct comparison to the known divergent p-series 1/n^1/2