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

Question

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

anonymous · Answer

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

anonymous · Answer

Hello?!

anonymous · Answer

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

anonymous · Answer

Do you know how to use the ratio test?!

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Ok, i'm working on it now

anonymous · Answer

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

anonymous · Answer

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.