1) So I need to prove that $\displaystyle (1+x)^n <= 1 + xn (x>= -1)$

I did $\displaystyle (1+x)^n+1 >= 1+x(n+1) $ ;then I just don't know where to go.

Then There are 2 sequence ones that I don't even know where to begin

a) Let Fn be the n-th term of the Fibonacci Sequence 1, 1, 2, 3, 5, 8,.. Defined by the rule:

F(n+2) = F(n) + F(n+1) [ Fn is F sub n]

prove by induction that F1+F2 +....+Fn $\displaystyle <=$2^(n+1)

b) The sequence a1, a2, a3, a4, ... an,... [again a sub n]

of positive integers defined by the rule:

a1 =1 a(n+1) = 3an (3 times a sub n) ( n = 1, 2,3,..) Prove that an = 3 ^(n-1) for n= 1,2,...