Find a power series representation for the function and dete

Find a power series representation for the function and determine the radius of convergence.

Solution

1/(1-x) = sum(x^n, n=0 to infinity), |x|<1 Replace x with -2x everywhere: 1/(1-(-2x)) = sum((-2x)^n, n=0 to infinity), |-2x|<1 Multiply by 3: 3/(1+2x) = 3 * sum((-2x)^n, n=0 to infinity), |2x|<1 Integrate both sides, and you are close to the power series representation for 3/(1+2x)