i'm supposed to be testing if this series converges or diverges

i'm assuming i should be using the alternate series test here

so.. i'm taking the limit, and getting lim as n->infinity of (j^1/2)/j+5 is eventually equal to (1/2 j^-1/2 )/ 6. i think that this limit equals zero, is that correct?

also, i'm wondering how i can easily prove that bn+1 < or equal to bn

thanks!