Solution
= Solution
Integrate the <geometric series> for $1/(1+x)$ from zero to $x$. The first three nonzero terms are
$$
\boxed{\ln(1+x)=x-\frac{x^2}2+\frac{x^3}3+O(x^4).}
$$
The resulting <Taylor series> converges for $|x|<1$.
= Solution
Integrate the <geometric series> for $1/(1+x)$ from zero to $x$. The first three nonzero terms are
$$
\boxed{\ln(1+x)=x-\frac{x^2}2+\frac{x^3}3+O(x^4).}
$$
The resulting <Taylor series> converges for $|x|<1$.