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

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SUMMARY

The Alternating Square Series Sum from 1 to 10201 is a finite series represented as 1 - 4 + 9 - 16 + 25 - ... - 10000 + 10201. The correct approach to solve this involves recognizing the pattern in the series and expressing it in summation form. The final calculated sum is 5151. However, there is a misconception regarding the convergence of the series; it is finite and does not exhibit the properties of an infinite series.

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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 ??
 
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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 ??
 
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.
 
nealjking said:
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.
 
nealjking said:
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.
 

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