Formal power series & Taylor series

I am honestly stuck on these problems - the subjects are neither covered in our textbook nor did I find anything after about an hour of googling:

Question 1: Using manipulations with formal power series, find the Taylor series of the following functions at $\displaystyle x=0$

(a) $\displaystyle \frac{1}{1+x+x^2}$

(b) $\displaystyle sin^{-1}(x)$

(c) $\displaystyle tanh(x)$

(d) $\displaystyle tan(x)$

Question 2: Apply Taylor's formula with Lagrange remainder to estimate the following number with given accuracy (a) cube root of 124 within 0.01 (b) pi within 0.001

Thanks a lot!