Math Help - Power Series Approximation.

1. Power Series Approximation.

Could someone explain the idea behind this problem?

Thanks!

I can substitute X^2 into the power series and multiply by X and then integrate, but what is the general idea behind finding the error?

2. Originally Posted by alin1916

Could someone explain the idea behind this problem?

Thanks!

I can substitute X^2 into the power series and multiply by X and then integrate, but what is the general idea behind finding the error?
The terms alternate in sign, which means that the error after a given number of terms is always less than (the absolute value of) the next term. So when you have done the integration, just take enough terms to ensure that the last one is less than 0.00005 in absolute value.

3. Originally Posted by Opalg
The terms alternate in sign, which means that the error after a given number of terms is always less than (the absolute value of) the next term. So when you have done the integration, just take enough terms to ensure that the last one is less than 0.00005 in absolute value.
So the term in which the absolute value of x evaluated to .5 is less than .00005, is the last term.

So that means if it's the 4th term, you would just write out the sum of the first four terms and leave it like that?

How exactly would you answer this question if it was on an exam?

Thanks!

4. I'd integrate it to get partial credit. Then I'd do some random stuff with finding $R_n(x)$ that'll get me the term with error less than 0.00005.

Out of curiosity, how would u find the term [analytically] that will give u error less than 0.00005?

5. Originally Posted by lilaziz1
I'd integrate it to get partial credit. Then I'd do some random stuff with finding $R_n(x)$ that'll get me the term with error less than 0.00005.

Out of curiosity, how would u find the term that will give u error less than 0.00005?
I guess you keep plugging and chugging until you get a < .00005 change between the Sn term and the Sn+1 term.

At least that's what I guess, I mean if the one hundred-thousandth term is the only one that's changing than the first 4 are accurate, right?