1.) Base case of : .
Now suppose is divisible by , then for some natural number .
Then .
Upon simplification we get . And we're done.
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