I'm left with these problems to do if anyone can help with any or all of them. Could you while helping me solve the problems try to explain in details especially with the proofs as this is one of my weaker sections in discrete maths. Thanks in advance.

1) Prove by mathematical induction that all positive integers n,

a)1*2+2*3+3*4...n(n+1)=n(n+1)(n+2)/3

b)1/(1*3)+1/(3*5)+1/(5*7)+...+1/(2n-1)(2n+1)=n/2n+1

c)(5^2n)-1 is divisible by 24

d) 1^2-2^2+3^2...((-1)^n+1)n^2=((-1)^n+1)n(n+1))/2

2) Prove by mathematical induction

a) that 2n+1<=2^n for n=3,4,...

b)Use part (a) in the proof that 2^n>=n^2 for n=4,5,...

3) Use mathematical induction to show that postage of 5 cents or more can be achieved by using only 2 cents and 5 cent stamps(as many of each is needed.