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

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Homework Help Overview

The problem involves determining the sum of an alternating series of squares from 1 to 10201, specifically the series 1 - 4 + 9 - 16 + 25 - ... - 10000 + 10201. The context is within the subject area of series and sequences in mathematics.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss identifying patterns in the series and suggest expressing it in summation notation. Some explore specific expressions for the sum, while others question the convergence of the series.

Discussion Status

The discussion includes various interpretations of the series, with some participants offering insights into potential approaches and others questioning the validity of the series' convergence. There is no explicit consensus on the methods or outcomes being discussed.

Contextual Notes

There is a debate regarding the nature of the series, with some participants asserting it is finite while others express concerns about convergence, indicating a need for clarity on the definitions and assumptions involved.

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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. [tex]\sum_{i=1}^n \left\{... \right\}[/tex]; 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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