Find the minimum value of N such that RN is smaller than the desired error. in n en? = 0.40488139857... an 2, error < 10-5, Σ n = 1 N = Compute the corresponding sum a, and compare it to the given estimate of the infinite series. (Round your answer to seven decimal places.) n = 1 Σ n = 1
Find the minimum value of N such that RN is smaller than the desired error. in n en? = 0.40488139857... an 2, error < 10-5, Σ n = 1 N = Compute the corresponding sum a, and compare it to the given estimate of the infinite series. (Round your answer to seven decimal places.) n = 1 Σ n = 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Find the minimum value of \( N \) such that \( R_N \) is smaller than the desired error.**
\[
a_n = \frac{n}{e^{n^2}}, \text{ error } < 10^{-5}, \quad \sum_{n=1}^{\infty} \frac{n}{e^{n^2}} = 0.40488139857 \ldots
\]
\( N = \ \) [ _____ ]
**Compute the corresponding sum \( \sum_{n=1}^{N} a_n \) and compare it to the given estimate of the infinite series. (Round your answer to seven decimal places.)**
\[
\sum_{n=1}^{N} a_n = \ \) [ _____ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc93930d1-cb91-4a53-93de-45d83c5caee7%2F74a115d9-97c6-4f2a-94ce-9269a64c563a%2F0u1pa5sh_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the minimum value of \( N \) such that \( R_N \) is smaller than the desired error.**
\[
a_n = \frac{n}{e^{n^2}}, \text{ error } < 10^{-5}, \quad \sum_{n=1}^{\infty} \frac{n}{e^{n^2}} = 0.40488139857 \ldots
\]
\( N = \ \) [ _____ ]
**Compute the corresponding sum \( \sum_{n=1}^{N} a_n \) and compare it to the given estimate of the infinite series. (Round your answer to seven decimal places.)**
\[
\sum_{n=1}^{N} a_n = \ \) [ _____ ]
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