Basically I'm trying to get this expression:
${(-1)^nn(n+1)\over2} + (-1)^{(n+1)}(n+1)^2$
In this form:
$(-1)^{(n+1)}(n+1)(n+2)\over2$
This is for a proof using mathematical induction, and I'm 99% sure that they DO equal each other. For some reason I'm having trouble doing this. What I've tried is setting 2 as the common denominator, and then factoring out a $(n+1)$ term and a $(-1)^{(n+1)}$ term.
After doing these steps, I ended up with:
$(-1)^{(n+1)}(n+1)(2n+1)\over2$
I'm not sure if I'm making a simple error, missing something, or if these two expressions are not equal to each other (but I seriously think that they are, because of the nature of the assignment that this question is from). Sometimes the simplest solutions are so hard to find.