So i got 8 questions for homework, i did 6. Here are the last two i'm having problems with. Thanks a lot guys.

12.12

Let (Sn) be a sequence of nonnegative numbers, and for each n, define

An = (1/n)(s1 + s2 + ... + sn)

(a) Show that liminfSn <= liminf An <= limsupAn <= limsupSn

Hint: for the last inequality show first that M > N implies sup{An : n>M} <= (1/M)(s1 + s2 + ... + sN) + sup{Sn : n>N}

(b) Show that if limSn exists, then limAn exists and limAn = limSn

12.14

Calculate:

(a) lim(n!)^(1/n)

(b) lim(1/n)(n!)^(1/n)

So yea, that last problem seems like a calc 3 problem, but nevertheless, i dont know how to do it.

Another thing that i probably should know already: Is adding sequences like adding vectors? as in you add corresponding terms of the sequences? What about multiplying two sequences, how is that done?

I may come back and post my solutions for the questions i did just to see what you guys think, but only if i can find the time, this homework is due monday. thanks again