Is there an error in this proof?

[mr_coffee]

Hello everyone, i was reviewing for the exam and I was working through this proof and I don't see how:

(2k+1)^2-(2k+1) + 3 = 4k^2+4k+1-2k-1+3 = 2(2k^2-k+1)+1

http://suprfile.com/src/1/3q9w3ud/Untitled-1[/URL] copy.jpg[/PLAIN]


But it is late so i maybe not seeing somthing.

 

[interested_learner]

If it is any help, there is an arithmetic error in the proof. Not that it makes any difference to the proof, but 4K-2K is +2K, not -2K.

 

[mr_coffee]

ahh okay that's what i wanted to make sure!
thanks!