UTECH
Feb 13, 2007, 09:51 AM
3 + 7 + 11 +... (4n - 1) = n(2n+1)
please submit full solution
galactus
Feb 13, 2007, 11:08 AM
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?