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α Σ n=1 1 2n + 1

α Σ n=1 1 2n + 1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please do the following for this series; 

A) Write this series in “expanded form”

(B) Write out the first few terms of the sequence of partial sums. 

This image represents an infinite series in mathematics. The series is expressed as: \[ \sum_{n=1}^{\infty} \frac{1}{2^n + 1} \] Explanation: - The symbol \(\sum\) denotes summation. - The index of summation is \(n\), which starts at 1 and goes to infinity, as indicated by the limits below and above the summation symbol, respectively. - The summand (term to sum) is \(\frac{1}{2^n + 1}\), meaning for each integer \(n\) starting from 1 and increasing indefinitely, you calculate \(2^n + 1\) and then take the reciprocal of that result. This series adds the reciprocal of \(2^n + 1\) for each \(n\) from 1 to infinity.
Transcribed Image Text:This image represents an infinite series in mathematics. The series is expressed as: \[ \sum_{n=1}^{\infty} \frac{1}{2^n + 1} \] Explanation: - The symbol \(\sum\) denotes summation. - The index of summation is \(n\), which starts at 1 and goes to infinity, as indicated by the limits below and above the summation symbol, respectively. - The summand (term to sum) is \(\frac{1}{2^n + 1}\), meaning for each integer \(n\) starting from 1 and increasing indefinitely, you calculate \(2^n + 1\) and then take the reciprocal of that result. This series adds the reciprocal of \(2^n + 1\) for each \(n\) from 1 to infinity.
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