I have difficulties in solving problems

1) Show that lim (1 + (1/2n))^n = sqrt e.

n-> oo

2)find lim (1+2/n)^n

n-> oo

3) lim (1 + 3/n) ^n

n-> oo

4) suppose 0 < Sn and Sn+1 < rSn, where r is a constant such that 0 < r < 1. Show that limn->oo Sn = 0.

5) suppose 0 < Sn and Sn+1 >= rSn, where r is a constant such that r > 1. Show that limn->oo Sn = +oo.