3 + 7 + 11 +... (4n - 1) = n(2n+1)
please submit full solution

Answer to question

I won't provide the full solution, but I can get you started.

#1. Show P_1 is true

#2. Assume P_k is true and then prove P_(k+1) is true.

4 is being added to each successive integer. The next integer in the sequence would be

4n+3. Add 4n+3 to each side.

3+7+11+... +(4n-1)+(4n+3)=n(2n+1)+4n+3

Does n(2n+1)+4n+3 give you (n+1)(2(n+1)+1)?

That's what you must show?