Find the Taylor series about c=0 and its interval of convergence?

F(x)= 1/(1-x) with the center at 0. Any help would be greatly appreciated

Find the Taylor series about c=0 and its interval of convergence?
Note that 1/(1-x) is the sum of a geometric series with ratio x, so it equals::


1 + x + x^2 + x^3 + x^4 + .... (which converges for absolute(x) less than 1.- so radius of convergence=1)





The long way is to compute the Taylor series directly:


f(0) = 1


Now find the derivatives of 1/(1-x) at x = 0 :


f'(0)= 1


f''(0)= 2


.f"'(0)= 3*2


...etc...


so you get f(x) = 1 + x + x^2 + x^3 + ...
Reply:F(x) = 1 +x +x^2 +.... ( -1%26lt;x%26lt;1).