- #1

RJLiberator

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## Homework Statement

The goal of this problem is to approximate the value of ln 2. We will use two different approaches: (a) First, we use the Taylor polynomial pn(x) of the function f(x) = lnx centered at a = 1.

- Write the general expression for the nth Taylor polynomial pn(x) for f(x) = lnx centered at a = 1.

**DONE**

- At x = 2, evaluate the size of the remainder Rn(2) = ln 2 − pn(2).

- What should n be so that you are sure that pn(2) approximates ln2 to two decimal

points? What is then the approximate value of ln 2 (up to two decimal points)?

## Homework Equations

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## The Attempt at a Solution

For part 1, I netted the (should be correct) answer of

ln(x) = Σ from n=1 to infinity of (-1)^(n+1)/n (x-1)^n

Now, I am completely stuck on part 2. At x=2, evaluate the size of the remainder Rn(2) = ln(2)-Pn(2).

Are there any examples out there? I am searching the internet for examples, but not much luck.

Thank you.