4 limit problems. I've done all the work. I just wanted to make sure I'm understanding this correctly, and hoping someone will double check that I'm doing the work right. Thanks for your time!

Find the limit of the sequences:

(1) = lim 1 + lim = 1 + 0 = 1

(2) = lim . I divided everything by n to get

= 2n^(-1/2) = 2/√n which goes to 0, and therefore the limit = 0.

[I already got #'s 3 and 4 checked. ]

(5) = lim = lim which goes to zero, and therefore the limit = 0.

(6) . I divided everything by 5^n:

. Since goes to zero then the expression becomes = 0. So the limit = 0.