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4. The Riemann zeta function is defined as ((x) = = n² (a) For which real numbers x is ((x) defined? (Or: for what values of x does this sum converge?) (b) Use the sum of the first 10 terms to estimate the sum of the series (2) = p-series with p = 2 (you will need a calculator). How accurate is your estimate? (ie. What is the upper bound on the remainder R,,.) 1/n², which is the

4. The Riemann zeta function is defined as ((x) = = n² (a) For which real numbers x is ((x) defined? (Or: for what values of x does this sum converge?) (b) Use the sum of the first 10 terms to estimate the sum of the series (2) = p-series with p = 2 (you will need a calculator). How accurate is your estimate? (ie. What is the upper bound on the remainder R,,.) 1/n², which is the

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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➜ ☺ T 21 4. The Riemann zeta function is defined as <(x) = (a) For which real numbers x is ((x) defined? (Or: for what values of x does this sum converge?) (b) Use the sum of the first 10 terms to estimate the sum of the series (2) = 1/n², which is the p-series with p = 2 (you will need a calculator). How accurate is your estimate? (ie. What is the upper bound on the remainder R.) (c) It turns out that ((2)=. Pretend that you do not know the numerical value of л. Using the formula Sn+ ++ for f(x) dx < s < S₁ + + f(x)dx what bounds do you get on the numerical value of 7²/6 from using the first 10 terms in the series? How close do you get to the numerical value of n? (Again you will need a calculator.) Filters Add a caption... × (1 > My group
Transcribed Image Text:➜ ☺ T 21 4. The Riemann zeta function is defined as <(x) = (a) For which real numbers x is ((x) defined? (Or: for what values of x does this sum converge?) (b) Use the sum of the first 10 terms to estimate the sum of the series (2) = 1/n², which is the p-series with p = 2 (you will need a calculator). How accurate is your estimate? (ie. What is the upper bound on the remainder R.) (c) It turns out that ((2)=. Pretend that you do not know the numerical value of л. Using the formula Sn+ ++ for f(x) dx < s < S₁ + + f(x)dx what bounds do you get on the numerical value of 7²/6 from using the first 10 terms in the series? How close do you get to the numerical value of n? (Again you will need a calculator.) Filters Add a caption... × (1 > My group
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