Using mathematical induction, prove that

Question

n + 4 < n + 9 for for every positive integers

Answer 1

prove by math induction n+4<n+9

let n=1,

1+4<1+9

5<10

let n=2

2+4 < 2+9

6<11

assume for n=k, k+4<k+9

try to show k+1+4 < k+1+9

substitute k+1 for n

k + 5 < k + 10

subtract k from both sides

5 < 10

therefore n+4<n+9 for all n>0 where n= a positive interger

QED