the series ((-1)^n+1)(x-2)^n)/n .... the interval of convergence is 1

Question

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.

anonymous · Answer

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

anonymous · Answer

$$|x-2|<1$$

anonymous · Answer

ok got it

anonymous · Answer

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

anonymous · Answer

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

saifoo.khan · Answer

Whenever free, http://openstudy.com/study#/updates/4f333c8be4b0fc0c1a0b72dd

anonymous · Answer

ok very smilar to the last one

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

so does not converge at x = 1

anonymous · Answer

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

anonymous · Answer

.ah! um a lot? haha.

anonymous · Answer

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

anonymous · Answer

thank you! another question...

anonymous · Answer

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

anonymous · Answer

keep posting

anonymous · Answer

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