1)Find with proof the sum from i = 1 to n of 2^i for each n >= 1. Find with proof the sum from i = 1 to n of 1/(i(i+1)) for each n >= 1. Prove that n! > 2^n for each n >= 4.

2)

Prove sqrt(2) is irrational.

Find with proof the sum of the first n odd positive integers.

3)

If A is the set of positive multiples of 8 less than 100000 and B is the set of positive multiples of 125 less than 100000, find |A intersect B|.

Find |A union B|.

There are 7 students on math team, 3 students on both math and CS team, and 10 students on math team or CS team. How many students on CS team?