How to Prove the (k+1) Step in PMI?

[sahilmm15]

I am stuck at the problem. Can't find out what to do next for proving for (k+1). Can you help me. Thanks[Moderator's note: moved from a technical forum.]

 

[sahilmm15]

Is it only for natural numbers? Why do you need induction, can't you just multiply out the bracket?

Only for natural numbers.

 

[Mark44]

What is the actual problem statement? The image you uploaded is almost impossible to read. As far as I can tell, it looks like you are to prove that $2n + 7 > (n + 3)^2$.

You don't need induction to prove this. You can do a proof by contradiction. I.e., assume that $2n + 7 \le (n + 3) ^2$. Expand the right side and from there get a contradiction.

 

[sahilmm15]

What is the actual problem statement? The image you uploaded is almost impossible to read. As far as I can tell, it looks like you are to prove that $2n + 7 > (n + 3)^2$.

You don't need induction to prove this. You can do a proof by contradiction. I.e., assume that $2n + 7 \le (n + 3) ^2$. Expand the right side and from there get a contradiction.

You read the problem right. Thanks for the answer.

 

[Mark44]

You read the problem right.

Well, lucky for me. The image you posted was nearly unreadable, which is why we ask that members posting homework problems type the equations or inequalities rather than post an image of their work. It's very rare that someone posts an image that can easily be read. Most images are unreadable due to illegible writing or poor lighting of the work being photographed, or a combination of the two.