Need help finding the sum of a sequence

I get.In summary, the conversation involves finding the sum of 2*(n-1)*x^(2n) by trying to integrate and then finding the derivative of the sum. However, there seems to be confusion on how to integrate when there is ^(2n) involved. One solution proposed is to replace ^(2n) with a variable k and use the formula for finding the integral of x^k. Another suggestion is to differentiate the sum or x^(2(n-1)) to find the correct answer.
  • #1
hyper
49
0
I have to sequence 2*(n-1)*x^(2n), I have tried integrating and then finding the sum and then derivating the sum, and I allmost get the right answer.

But I think I am integrating wrong since I really don't know of the integrate when I have ^(2n), and not only n.

please help
 
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  • #2
When you integrate x2n Just write k=2n. Then integral of xk is xk+1/(k+1) = x2n+1/(2n+1)
 
  • #3
You know, I presume, that the integral of xn is 1/(n+1) xn+1+ C where n can be any number. Well, 2n is just a number! The integral of x2n is 1/(2n+1) x2n+1+ C. So the integral of 2(n-1)x2n is 2((n-1)/(2n+1))x2n+1. But I don't think that will help you find the sum!
 
  • #4
How should I find the sum then?
 
  • #5
differentiate sum x^2n and see what you get. Or better yet, differentiate x^(2(n-1))
 

1. What is a sequence?

A sequence is a set of numbers that follow a specific pattern or rule. Each number in the sequence is called a term.

2. How do I find the sum of a sequence?

To find the sum of a sequence, you need to add up all the terms in the sequence. This can be done by hand or with a calculator.

3. What is the formula for finding the sum of a sequence?

The formula for finding the sum of a sequence is (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term.

4. Can I use this formula for any type of sequence?

No, this formula only works for arithmetic sequences. For other types of sequences, you will need to use a different formula or method to find the sum.

5. Are there any shortcuts or tricks for finding the sum of a sequence?

Yes, there are various shortcuts and tricks for finding the sum of a sequence, such as using the sum formula for an arithmetic series, or using patterns in the sequence to simplify the calculation. It is always helpful to look for these shortcuts when solving a sum of a sequence problem.

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