Mathematical Induction Question (1 Viewer)

[furnz]

Can someone help me out with the K+1 steps on this question please

Prove 12^k >= 5^k + 7^k

Thanks

 

[Iruka]

The thing to note is that 12 is bigger than either 5 or 7.

Thus

12^(k+1)=12.12^k
>=12.5^k+12.7^k (by the inductive hypothesis)
> 5.5^k + 7.7^k
= 5^(k+1)+7^(k+1)

as required.

 

[furnz]

thanks