# Solve The Series

1. Jun 4, 2013

### klen

$$S_n = \sum_{k=1}^ {4n} {(-1)^\frac{k(k+1)}{2}} {k^2}$$.

Then Sn can take what values among:
1056, 1088, 1120, 1332

2. Jun 4, 2013

### tiny-tim

hi klen!

simplest way is probably to do the sum for 4m-3,4m-2,4m-1,4m (only) first …

what do you get?

3. Jun 4, 2013

### HallsofIvy

Staff Emeritus
Did you, for example, notice that every time n increases by 1, the sum has 4 new terms, two negative and two positive? Do you notice that for n= 1, so there are 4 terms, the sum is 20= 4(5) and when n= 2, so there are 8 terms, the sum is 72= 8(9)?