Problem 1:

Define the binomial coefficient

n by

r

n = n! / (r!(n-r)!) for r = 0,1,2,...., n

r

problem: show that

n

r

+

n

r-1

=

n+1

r

for r = 0,1,2,...,n

problem 2:

Use induction to prove Bernoulli's inequality:

If 1+x>0, then (1+x)^n >= 1+nx for all n (element) of N

N is the set of positive integers, natural numbers