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Find the Taylor series generated by $f$ at $x=a$.$$f(x)=2^{x}, \quad a=1$$

$$\sum_{n=0}^{\infty} 2(\ln 2)^{n} \frac{(x-1)^{n}}{n !}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

14:11

In mathematics, the partial sums of a series are the sums of all terms of the series except possibly the first and last.

01:45

Find the Taylor series gen…

02:28

00:45

02:03

For the function f of x, equal to 2 to the power of x behalf and derivative x, is equal to 2. To the power of x is 2 to the power of so derivative .1 is equal to 2 times n 2 to the power of to the tenor series at x, equals to 1 is f of x equal to sum, and from 0 to infinity 2 times, l N 2 to the puffin x, minus 1 to the power n over n factorial.

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