### Home > APCALC > Chapter 12 > Lesson 12.2.1 > Problem12-70

12-70.

Use sigma notation to write the Maclaurin series, $p(x)$, for $f(x) = \ln(x + 1)$.

From problem 12-30, the Taylor polynomial for $f(x) = \ln(x)$ centered at $x = 1$ is:

$\ln(x)\approx p(x)=(x-1)-\frac{(x-1)^2}{2}+\frac{(x-1)^3}{3}-\frac{(x-1)^4}{4}+...+\frac{(x-1)^n}{n}+...$

Substitute $(x + 1)$ for all $x$ in the Taylor polynomial above.