For each n ∈ N, let Am (x) = {1/2" if 1/2" < x<1if 0

Name: For each n ∈ N, let Am (x) = {1/2" if 1/2" < x<1if 0
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Description: For each n ∈ N, let Am (x) = {1/2" if 1/2" < x<1if 0

Given: hnx=12nif 12n<x≤10if 0≤x≤12n; n∈N and Hx=∑n=1∞hnx. We have to show that H is integrable…

Answered: Am (x) = { 1/2" if 1/2" < x<1 if 0

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter11: Rational And Irrational Numbers

Section: Chapter Questions

Problem 23CLR

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For each n ∈ N, let

Am (x) = {
1/2" if 1/2" < x<1
if 0<x< 1/2"
and set H(r) = E n(x). Show H is integrable and compute fo H.
n=D1

Expert Solution

Step 1

Given:

$h_{n} (x) = \{\begin{cases} \frac{1}{2^{n}} & if \frac{1}{2^{n}} < x \leq 1 \\ 0 & if 0 \leq x \leq \frac{1}{2^{n}} \end{cases}$ ; $n \in N$ and $H (x) = \sum_{n = 1}^{\infty} h_{n} (x)$ .

We have to show that H is integrable and compute $\int_{0}^{1} H$ .

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