Solving Infinite Sums/Series: Kid Tutoring Homework

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In summary, the conversation is about someone trying to figure out an infinite sum question for a student they tutor. They have derived a formula for the sum and are having trouble integrating it to find the solution. They receive a hint to integrate and try to use the sigma and infinity symbols, but realize the student has not learned integration yet. They then try to use a different method but still cannot arrive at the correct answer. Finally, they decide to just tell the student to trust them and give the correct answer.
  • #1
muso07
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Homework Statement


Figuring out an infinite sum question for the kid I tutor... it's late and my brain's not functioning well. I think I'm overcomplicating the question, but I can't figure it out.

The the sum of the following infinite series:
S = 1+3x+5x^2+...

Homework Equations



The Attempt at a Solution


I got that tn = [tex](2n-1)x^{n-1}[/tex]

Which means the sum is
[tex]\Sigma (2n-1)x^{n-1}=2\Sigma nx^{n-1} - \Sigma x^{n-1} = 2\Sigma nx^{n-1} - \frac{1}{1-x}[/tex]

And here is where I get stuck...
 
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  • #2
Hi muso07! :smile:

Hint (for ∑ nxn-1):

integrate. :wink:
 
  • #3
Hm, the kid's in Year 11 so he hasn't done integration yet...

But when you integrate, you get x^n. Then [tex]lim_{(a\rightarrow\infty)} [x^{n}]^{a}_{1}= lim_{(a\rightarrow\infty)}x^{a}-x=-x[/tex]
This isn't right, though... I feel like such an idiot. :P
 
  • #4
(have a sigma: ∑ and an infinity: ∞ and try using the X2 and X2 tags just above the Reply box :wink:)

No, you want d/dx lima->∞ (∑xn) :smile:
 
  • #5
You beat me to replying. Is the sum (1+x)/(1-x)^2?
 
Last edited:
  • #6
Nevermind, I'm just going to tell him to believe me and it shall be great.

Thanks for all your help!
 

What is an infinite sum/series?

An infinite sum/series is a mathematical concept where a sequence of numbers is added together infinitely. This means that there is no limit to the number of terms in the sum/series.

Why is it important to know how to solve infinite sums/series?

Knowing how to solve infinite sums/series is important because it is a fundamental concept in mathematics and has many real-world applications. It also helps in understanding more complex mathematical concepts.

What are the different methods for solving infinite sums/series?

There are various methods for solving infinite sums/series, including the geometric series method, the telescoping series method, the ratio test, and the integral test. Each method has its own set of conditions and can be used depending on the type of infinite sum/series.

What are some common mistakes to avoid when solving infinite sums/series?

Some common mistakes to avoid when solving infinite sums/series include forgetting to check for convergence, using the wrong method for a particular series, and not checking the validity of the conditions for a particular method.

How can I improve my skills in solving infinite sums/series?

To improve your skills in solving infinite sums/series, practice is key. Start with simpler series and gradually move on to more complex ones. Also, make sure to understand the conditions and limitations of each method and practice applying them to various series.

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