$$\sum_{i=1}^n(-1)^{i+1}i^2 = (-1)^{n+1}\sum_{i=1}^n i.$$
im trying to prove thi by induction. im starting from the LHS and trying to show the RHS after assuming true for n=k
$$\sum_{i=1}^{k+1}(-1)^{i+1}i^2 = (-1)^{k+1}\sum_{i=1}^k i + (-1)^{k+2}(k+1)^2$$
Is this right so far because im finding it hard to manipulate this to what i want. im ending up with a $k^2$ term which i dont know what to do with.
Use formula for $\sum_{i=1}^k i$