# Thread: Maclaurin series

1. ## Maclaurin series

The function of defined by f(x)=1/(1+x³). The Maclaurin series for f is given by 1-x³+x^6-x^9+...+(-1)^n x^3n+...,
which converges to f(x) for -1<x<1.

Find the first four nonzero terms and the general term for the Maclaurin series representing ∫ f(t) from 0 to x.

Thank you, guys!

2. Originally Posted by jwu
The function of defined by f(x)=1/(1+x³). The Maclaurin series for f is given by 1-x³+x^6-x^9+...+(-1)^n x^3n+...,
which converges to f(x) for -1<x<1.

Find the first four nonzero terms and the general term for the Maclaurin series representing ∫ f(t) from 0 to x.

Thank you, guys!
so do it ...

$\int_0^x 1-t^3+t^6-t^9+ ... \, \,dt
$