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Using the remainder estimate for the integral test, estimate the error involved in 6n approximating the sum of the series using the first 6 terms (n² + 1)4 n=1 (A) error at most 503 2 (B) error at most 503 36 (C) error at most 37 (D) error at most (E) error at most (F) error at most . F B

Using the remainder estimate for the integral test, estimate the error involved in 6n approximating the sum of the series using the first 6 terms (n² + 1)4 n=1 (A) error at most 503 2 (B) error at most 503 36 (C) error at most 37 (D) error at most (E) error at most (F) error at most . F B

Advanced Engineering Mathematics
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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Using the remainder estimate for the integral test, estimate the error involved in 6n approximating the sum of the series using the first 6 terms (n² + 1)4 n=1 (A) error at most 503 2 (B) error at most 503 36 (C) error at most 37 (D) error at most (E) error at most (F) error at most . F B
Transcribed Image Text:Using the remainder estimate for the integral test, estimate the error involved in 6n approximating the sum of the series using the first 6 terms (n² + 1)4 n=1 (A) error at most 503 2 (B) error at most 503 36 (C) error at most 37 (D) error at most (E) error at most (F) error at most . F B
Expert Solution
Step 1

Let an=f(n) and ∑an is convergent by integral test. Let Rn=S-Sn, where, S represents the sum of infinitely many terms and Sn represents the sum of first n terms. 

Then it can be written that: ∫n+1∞f(x)dx≤Rn≤∫n∞f(x)dx.

 

It is known that ∫abxndx=1n+1bn+1-an+1 .

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