anonymous 5 years ago For the following power series determine the interval of convergence S = (3x^2 ÷ 4 • 7) +( 5x^4 ÷ 7 • 9) + (7x^6 ÷10 • 11) + . . .

1. anonymous

Is it 3x^2/(4*7) OR (3x^2/4)*7?

2. anonymous

Hello?!

3. anonymous

it is 3x^2/(4*7) AnwarA, I'm sorry i was doing other problems. I'll be waiting my friend

4. anonymous

Do you know how to use the ratio test?!

5. anonymous

Yes i know the basics like convergence and divergence based on the value 1

6. anonymous

Let me help you first with writing the series in its standard from; ${3x^2 \over 4(7)}+{5x^4 \over 7(9)}+{7x^6 \over 10(11)}+...=\sum_{n=1}^{\infty}{(2n+1)x^{2n} \over (3n+1)(2n+5)}$

7. anonymous

That's good. Now do the test, and find the limit. Tell me what you get!

8. anonymous

Ok, i'm working on it now

9. anonymous

all the terms cancell out and i am left with 1 which i added to Un and therfore test fails

10. anonymous

Well, actually you will be left with |x|. Then your interval of convergence should be |x|<1. That's -1<x<1. Then you should test the endpoint -1 and 1.