anonymous 4 years ago the series ((-1)^n+1)(x-2)^n)/n .... the interval of convergence is 1<x<3, but i need help checking the convergence of the endpoints.

1. anonymous

another end point one, this time i do it with paper before typing

2. anonymous

$|x-2|<1$

3. anonymous

ok got it

4. anonymous

now we try replacing x by 1 btw you have done all the hard work, the rest should be the easy part

5. anonymous

at x=1 i think it is $\sum_{?}^{?} (-1)^{n+1}(-1)^{n}\div n$ ???

6. saifoo.khan
7. anonymous

ok very smilar to the last one

8. anonymous

but this time we don't do anything stupid $(-1)^{n+1}(-1)^n=(-1)^{2n+1}=-1$

9. anonymous

on account of $2n+1$ is odd.

10. anonymous

so does not converge at x = 1

11. anonymous

what do you want to bet it does converge at x = 3?

12. anonymous

.ah! um a lot? haha.

13. anonymous

yeah well we can just about visualize it because it is the same as the last one. this time you get $(-1)^{n+1}\times 1=(-1)^{n+1}$so we are in good shape

14. anonymous

thank you! another question...

15. anonymous

this one alternates in other words, whereas the other one does not

16. anonymous

keep posting

17. anonymous

you got zarkon watching so if i mess up he will step in wish he had stepped in to the last one so i wouldn't have made a fool out of myself