Thread: what taylor series tables should I memorize?

1. what taylor series tables should I memorize?

Hi, all.

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

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

...based on his knowledge that:

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

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:

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

To here:

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

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

Thanks!

2. Taylor series - Wikipedia, the free encyclopedia

The above link contains a pretty comprehensive list of Taylor series and their usages. To be honest, you would be much better off teaching yourself how to derive the Taylor series for any function that interests you as memorising a large amount of series is going to be quite difficult as a lot of them look very similar when written in concise form