Question

Using principle of mathematical induction prove that 4n^2+15n-1 is divisible by 9 .

Answer 1

let the statement be s(n)=4n^2+15n-1 divisible by 9
to prove that s(n) is true n=1:
4(1)^2+15(1)-1=4+15-1=18
it is divisible by 9
s(n) is true for n=1
assume that s(n) is true for n=k
4k^2+15k-1=9m (m is some internet)
4k^2=9m-15k+1
to prove that s(n) is true for n=k+1
4(k+1)^2+15(k+1)-1
=4k^2+8k+4+15k+15-1
=9m-15k+1