Hi, all.

In this recent post, TwistedOne151 was able to easily deduce that:

$\displaystyle \frac{x^n}{1+x}=\sum_{k=0}^{\infty}(-1)^kx^{n+k}$

...based on his knowledge that:

$\displaystyle \frac{1}{1+x}=\sum_{k=0}^{\infty}(-x)^k$

So, apparently I should know at least that series--but what others should I learn? Is there perhaps an online table of taylor/maclaurin series that I should commit to memory?

Also--and this is just a random question from that same thread--how did he go from here:

$\displaystyle \sum_{k=0}^{\infty}\frac{(-1)^k}{n+k+1}$

To here:

$\displaystyle (-1)^n\left[\sum_{k=0}^{\infty}\frac{(-1)^k}{k+1}-\sum_{k=0}^{n-1}\frac{(-1)^k}{k+1}\right]$

...? Is that some kind of identity I should know?

Thanks!