Thread: find the power series representation

need help to find the power series representation, and determine interval of convergence

heres the equation:

f(x) = 1/(1+x)

trouble with these. please help.

Originally Posted by rcmango

need help to find the power series representation, and determine interval of convergence

heres the equation:

f(x) = 1/(1+x)

trouble with these. please help.

f(x) = 1/(1-x) is the geometric series.

f(x) = 1+x+x^2+x^3+... for |x|<1

Substitute -x for x (by handwaving),

f(-x) = 1/(1+x) = 1-x + x^2 - x^3 + x^4 - ... for |-x|=|x|<1