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V8(4n)!(1103 +26390n) 9801 396 (n!)4 (b) The partial sums for this series are S, Use a calculator to evaluate and . and write down as many digits as your calculator can display. How many digits are the same as the digits of r? Note: 7 3.1415926535 8979323846 2643383279...

V8(4n)!(1103 +26390n) 9801 396 (n!)4 (b) The partial sums for this series are S, Use a calculator to evaluate and . and write down as many digits as your calculator can display. How many digits are the same as the digits of r? Note: 7 3.1415926535 8979323846 2643383279...

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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Q2b
V8(4n)!(1103 + 26390n) 9801-3964 (n!)4 2. Now consider the series This series was discovered by the extraordinary Indian mathematician Srinivasa Ramanujan (1887-1920). This series converges to and it is much more difficult than finding the sum of the series in problem 1.) This series has been used to compute n to over 17 million digits (which was a world record at the time).. (You do NOT need to prove that, V8(4n)!(1103 + 26390n) 9801 396" (n!)4 (a) - Use any test for convergence/divergence to show that the series converges. V8(4n)!(1103 + 26390n) 9801 · 3964"(n!)4 (b) The partial sums for this series are S = > %3D Use a calculator to evaluate and . and write down as many digits as your calculator can display. How many digits are the same as the digits of n? Note: T 3.1415926535 8979323846 2643383279... Bonus: Watch the movie "The man who knew infinity" (2015) about the life of Srinivasa Ramanujan.
Transcribed Image Text:V8(4n)!(1103 + 26390n) 9801-3964 (n!)4 2. Now consider the series This series was discovered by the extraordinary Indian mathematician Srinivasa Ramanujan (1887-1920). This series converges to and it is much more difficult than finding the sum of the series in problem 1.) This series has been used to compute n to over 17 million digits (which was a world record at the time).. (You do NOT need to prove that, V8(4n)!(1103 + 26390n) 9801 396" (n!)4 (a) - Use any test for convergence/divergence to show that the series converges. V8(4n)!(1103 + 26390n) 9801 · 3964"(n!)4 (b) The partial sums for this series are S = > %3D Use a calculator to evaluate and . and write down as many digits as your calculator can display. How many digits are the same as the digits of n? Note: T 3.1415926535 8979323846 2643383279... Bonus: Watch the movie "The man who knew infinity" (2015) about the life of Srinivasa Ramanujan.
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