1. The problem statement, all variables and given/known data 1. Find a power series for (1-x)^(-1/2) 2. Find a power series for (1-x^2)^(-1/2) 3. Find a power series for arcsin(x) 2. Relevant equations Binomial series, (1+x)^k= 1 + kx + k(k-1)x^2/2!+ k(k-1)(k-2)x^3/3!+.... 3. The attempt at a solution for 1., I have 1+ (-1/2)(-x) + (-1/2)(-1/2-1)(-x)^2/2! + (-1/2)(-1/2-1)(-1/2-2)(-x)^3/3!+.... Simplified, 1+ x/2 +3x^2/8+ 15x^3/48 + 35x^4/128+.... From here, I am having trouble finding the general term. Once I can find that, the rest is easy...just use x^2 instead of x for (2) and integrate the series to get arcsin(x) for (3). I know I could look up a power series for arcsin(x) in a table or website but the point is to get it using the binomial series.