# Homework Help: Summation of the series

1. Nov 12, 2012

### Kartik.

S = 12-22+32-42.......+20092

Attempt=

S = (1+2)(1-2)+(3+4)(3-4)+.....+(2007-2008)(2007+2008) [can we write this as -(1+2+3+4+5....2008) if yes, then why ?) +20092
Stuck after this.

2. Nov 12, 2012

### Saitama

Do you know the summation of:
12+22+32+42+......+n2

That would be of help here.

3. Nov 12, 2012

### Mentallic

Yes you can write it as -(1+2+...+2008)+20092 because

(1+2)(1-2) = -(1+2)
(3+4)(3-4) = -(3+4)
...

And finally, we factored 20072-20082 but left out the 20092 term so we need to add that term in at the end.

Now, do you know the formula to sum the first n natural numbers?

Hint:

1+2+3+...+(n-2)+(n-1)+n

= (1+n) + (2+(n-1)) + (3+(n-2))+...

4. Nov 12, 2012

### Bonaparte

Just to give you a greater hint to support Mentallic, draw out the numbers from 1 to n
1+2+3+4....n-3+n-2+n-1+n, now notice, like Mentallic said, how 1+n = n-1+2 = n-2+3, so all those pairs have the same value, and when you have x things with value y, the result is.....

Bonaparte