Taylor series of $\ln(1+x+x^2+...+x^{10})$

Question

I have to find Taylor series of $\ln(1+x+x^2+...+x^{10})$. I have a clue that I write like the two difference of logarithm but I do not how.

Any help?

Answer 1

Recall the formula for a finite geometric series:

$$1+x+x^2 + \cdots + x^n = \frac{1-x^{n+1}}{1-x}$$

Take $n=10$ and you can apply this to your problem fairly readily.