I think you should assume that |x| < 1 (otherwise the first term of the series will not be defined, being the log of a negative number).
Now use the power series expansion for –log(1–t) (valid when 0<t<1):
Substitute to see that and use the comparison test with .
Thanks for that Opalg. This was incidently one of the routes I took. But, I convinced myself otherwise as my problem here is that the comparision test is set for positive series. So, we have to set (which is what we already have). However, for some fixed , it's not always the case that
what do I do/say in my argument to fix this?
Thanks in advance,
HTale