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

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In summary: The correct answer is 10201.In summary, the conversation was about determining the sum of a series of numbers and finding a pattern to solve it. The final answer is 10201. The discussion also touched upon the concept of infinite series and convergence.
  • #1
Lord Dark
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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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  • #2
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.
 
  • #3
i got an idea that Sum (1,51) (2x-1)^2-(2x-2)^2 = 5151
is it right ??
 
  • #4
The number is right. If you are clear how to get it from your expression, you should be ok.
 
  • #5
thanks very much :D , i just needed to be sure of my way
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 

What is the sum of two numbers?

The sum of two numbers is the result of adding the two numbers together.

What is the formula for determining the sum of a series of numbers?

The formula for determining the sum of a series of numbers is: sum = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term.

What is the difference between an arithmetic sum and a geometric sum?

An arithmetic sum is the sum of a series of numbers that have a constant difference between them, while a geometric sum is the sum of a series of numbers that have a constant ratio between them.

How do you determine the sum of an infinite series?

The sum of an infinite series can be determined by finding the limit of the partial sums of the series as the number of terms approaches infinity.

How can the sum of a series be used in real-world applications?

The sum of a series can be used in a variety of real-world applications, such as calculating the total cost of items purchased with tax, finding the total distance traveled in a journey with multiple stops, or determining the total population of a species over multiple generations.

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