Write the first five terms of the sequence. (Assume that n begins with 1 .) an=((-1)^n+1)/(n^2

Name: Problem 22, Chapter 9: Precalculus
Uploaded: 2021-02-07T14:16:39-08:00
Duration: 1 min 57 s
Channel: Anurag Kumar
Description: Write the first five terms of the sequence. (Assume that n begins with 1 .) an=((-1)^n+1)/(n^2+1)

step 1 In this problem of sequence we have given that a n equals to this is minus 1 to the power n plus

Question

Write the first five terms of the sequence. (Assume that $n \text { begins with } 1 .)$ $$a_{n}=\frac{(-1)^{n+1}}{n^{2}+1}$$

   Write the first five terms of the sequence. (Assume that $n \text { begins with } 1 .)$
$$a_{n}=\frac{(-1)^{n+1}}{n^{2}+1}$$

Precalculus

Ron Larson 10th Edition

Chapter 9, Problem 22

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Solved by Expert Anurag Kumar

02/07/2021

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Write the first five terms of the sequence. (Assume that $n \text { begins with } 1 .)$ $$a_{n}=\frac{(-1)^{n+1}}{n^{2}+1}$$

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Key Concepts

Sequence

A sequence is an ordered collection of elements defined by a specific rule or formula where each term corresponds to a distinct index. Understanding sequences involves recognizing how a sequence is generated and analyzing patterns or properties that emerge from its terms.

Alternating Sequence

An alternating sequence is one in which the signs of the terms change between positive and negative. This is typically achieved using a factor such as (-1) raised to a function of the index, which ensures that the terms alternate as the index increases.

Term Evaluation

Evaluating a term in a sequence requires substituting a specific index into the sequence’s formula and simplifying the resulting expression. This process helps in determining individual values and understanding the behavior of the sequence over its domain.

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