Problem 43

Question

Define a power series centered at $c$.

Step-by-Step Solution

Verified

Answer

A power series centered at $ c $ is defined by $ \sum_{n=0}^{∞} c_n (x - c)^n $

1Step 1: Define a general power series

Firstly, we need to understand a general power series. A power series is an infinite series of the form $ \sum_{n=0}^{∞} c_n (x - a)^n $, where $ c_n $ are the coefficients of the series, $ x $ is the variable, and $ a $ is the center of the series.

2Step 2: Center the power series at c

To center a power series at any point $ c $, we replace $ a $ with $ c $ in the general power series. This gives us the power series centered at $ c $, which is defined by $ \sum_{n=0}^{∞} c_n (x - c)^n $

Problem 43

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