# Determine the following sum,,

## Homework Statement

hi guys ,, i hope you all are fine ,,
i have a problem with this question :
Determine the following sum:
1-4+9-16+25-...-10000+10201

## The Attempt at a Solution

i don't know where even to start ,, can anyone give me an idea how to solve problems like these ??

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Do you see a pattern between the numbers? Try to write it in summation form i.e. $$\sum_{i=1}^n \left\{... \right\}$$; after you see the pattern, you should know what n is. Then you can find the sum.

i got an idea that Sum (1,51) (2x-1)^2-(2x-2)^2 = 5151
is it right ??

Dick
Homework Helper
The number is right. If you are clear how to get it from your expression, you should be ok.

thanks very much :D , i just needed to be sure of my way

You're wasting your time: That series does not and cannot converge. How could it? The terms get bigger and bigger.

Read up on what it means for an infinite series to converge.

You're wasting your time: That series does not and cannot converge. How could it? The terms get bigger and bigger.
No, you're wrong there's no infinite series.

Read up on what it means for an infinite series to converge.

Mark44
Mentor
You're wasting your time: That series does not and cannot converge. How could it? The terms get bigger and bigger.

Read up on what it means for an infinite series to converge.
As Dirk pointed out, and as you can see in the OP, this is a finite sum.