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) http://www.cramster.com/Answer-Board...1250002888.gifhttp://www.cramster.com/Answer-Board...8125003460.gif= lim 1 + lim http://www.cramster.com/Answer-Board...1875005327.gif= 1 + 0 = 1

(2) http://www.cramster.com/Answer-Board...1250002888.gif http://www.cramster.com/Answer-Board...4375003747.gif= lim http://www.cramster.com/Answer-Board...9062508324.gif. I divided everything by n to get

http://www.cramster.com/Answer-Board...0000008526.gif= 2n^(-1/2) = 2/√n which goes to 0, and therefore the limit = 0.

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

(5) http://www.cramster.com/Answer-Board...1250002888.gif http://www.cramster.com/Answer-Board...5000002910.gif= lim http://www.cramster.com/Answer-Board...1562507038.gif= lim http://www.cramster.com/Answer-Board...2812506446.gif which goes to zero, and therefore the limit = 0.

(6) http://www.cramster.com/Answer-Board...1250002888.gifhttp://www.cramster.com/Answer-Board...5156250477.gif. I divided everything by 5^n:

http://www.cramster.com/Answer-Board...9375001840.gif. Since http://www.cramster.com/Answer-Board...6250000423.gif goes to zero then the expression becomes http://www.cramster.com/Answer-Board...6875007692.gif= 0. So the limit = 0.