Is the Alternating Square Series Sum from 1 to 10201 Solvable?

[Lord Dark]

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

Homework Equations

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 ??

 

[konthelion]

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.

 

[Lord Dark]

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

 

[Dick]

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

 

[Lord Dark]

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

 

[nealjking]

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.

 

[dirk_mec1]

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.

Maybe YOU should read better.

 

[Mark44]

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.