Originally Posted by

**blaze** Have some trouble completing these questions:

Any help will be greatly appreciated:

1 Use mathematical induction to prove that 5^n+9^n+2 is divisible by 4 for all n>0

2a) use mathematical induction to prove that:

1/(2r-1)(2r+1)=n/2n+1 for all n>0

b) Hence show that the sum of the first (n +1) terms of the series

1/3+1/15+1/35+1/63+....is (n+1)/(2n+3)

3) (1)(1!)+(2)(2!)+(3)(3!)+...+(n)(n!)=(n+1… where n>0 Find the minimum number of terms of the series for the sum to exceed 10^9