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Use the Maclaurin series for $ e^x $ to calculate $ 1/\sqrt[10]{e} $ correct to five decimal places.

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Missouri State University

Campbell University

Baylor University

Idaho State University

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.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

04:05

Use the Maclaurin series f…

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the problem is used like our theories or into bikes to compute one over each one over ten cracked ege of decimal places suffused behalf Macarons Siri's for into axe is because to sound from zero to twenty, I have to end over end factorial. Now that should compute one over Interconnected you two one over ten. So we need to light is equal to negative one. Over. Yeah, so what end Because. Well, Father, we have no to one one returned to father over off material. This is about two point three halves. Tend to negative it. So we have you need to connect. You want ten? This is one over into. Oh, my. This is about one plus negative one of ten. Plus next to squire over two us. Negative. One cube, three factorial us negative. While ten. It's part of war for Victoria, which is about zero point my cereal war war

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