I dont want just answers, I am looking for a good explanation to make it easier.

1. Prove or disprove that 1 + 1/4 + 1/9 + ... + 1/100 < 2 - 1/10

2. Prove that f^kf^n + f^k+1f^n+1 = f^n+k+1 for all nonnegative integers n, where k is a nonnegative integer and f^i denotes the ith Fibonacci number.

3. Give a recursive definition of the functions max and min so that max(a1,a2,...an) and min (a1,a2,...an) are the maximum and minimum of the n numbers (a1,a2,...,an) respectively.

4. Give a recursive definition of the each of these sets of ordered pairs of positive integers:

a) S = {(a,b)|a and b are positive integers, and (a+b) is even};

b) S={a.b)|a and b are positive integers, and (a+b) is odd, and 3|b};