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Find the Maclaurin series for the functions$$\frac{2+x}{1-x}$$

$$2+\sum_{n=1}^{\infty} 3 x^{n}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

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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.

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

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Find the Maclaurin series …

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For the function 2 plus x, over 1 minus x point so first we can rewrite this function as negative 1 minus x plus 3 over 1 x, which is equal to 3 times 1 over 1 minus x minus 1 point, and we know that mac laurin series Of 1 over 1 minus x is some and from 0 to infinity x to the power of n. Then this is maccleary series of function. This function.

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