Use the sum of the first ten terms to approximate the sum of the series L n√n²-1 n = 2 (Hint: Use trigonometric substitution. Round your answers to three decimal places.) sum 1.822 error 0.273 X Estimate the error by taking the average of the upper and lower bounds given by Theorem 16.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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It is not 0.300, 0.287, 0.301, or 0.273.

Theorem 16. Remainder Estimate for the Integral Test
Let f(x) be a positive-valued continuous decreasing function on the interval [1, ∞) such that
f(n) = an for every natural number n. If the series Σan converges, then
n=1
n+1
f(x) dx ≤ R₂ ≤
<
n
∞
f(x)dx
Transcribed Image Text:Theorem 16. Remainder Estimate for the Integral Test Let f(x) be a positive-valued continuous decreasing function on the interval [1, ∞) such that f(n) = an for every natural number n. If the series Σan converges, then n=1 n+1 f(x) dx ≤ R₂ ≤ < n ∞ f(x)dx
Use the sum of the first ten terms to approximate the sum of the series
n = 2
(Hint: Use trigonometric substitution. Round your answers to three decimal places.)
sum
error
1.822
0.273
3
n√√√n²
ny
X
. Estimate the error by taking the average of the upper and lower bounds given by Theorem 16.
- 1
Transcribed Image Text:Use the sum of the first ten terms to approximate the sum of the series n = 2 (Hint: Use trigonometric substitution. Round your answers to three decimal places.) sum error 1.822 0.273 3 n√√√n² ny X . Estimate the error by taking the average of the upper and lower bounds given by Theorem 16. - 1
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