The following function has a series of the form the sum from n=0 to infinity of c(subn)x^n. Calculate the coefficients c(subn) and express the power series in summation notation.

Question

f(x)=(pi*x)/(pi*x+1)
Thank you so much for your help!!!!

Answer 1

f(x) = 1 - 1/(pi*x+1)
f' = pi/(pi*x+1)^2
f'' = -2/(pi*x+1)^3
...

f(x) = 0 + pi*x - (pi*x)^2 + (pi*x)^3 - ...
c_n = -(-1)^n pi^n = -(-pi)^n

Answer 2

Thank you soooooooo much!!!!