V8(4n)!(1103 + 26390n) 9801 · 3964n (n!)4 2. Now consider the series > This series was discovered by the extraordinary Indian n=0 mathematician Srinivasa Ramanujan (1887-1920). This series converges to 1 (You do NOT need to prove that, and it is much more difficult than finding the sum of the series in problem 1.) This series has been used to compute T to over 17 million digits (which was a world record at the time). V8(4n)!(1103 + 26390n) 9801 · 3964n (n!)4 (a) ks) Use any test for convergence/divergence to show that the series n=0 converges. V8(4n)!(1103 + 26390n) 9801 - 3964" (n!)ª (b) The partial sums for this series are Sk = ). n=0 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 ? Note: T 3.1415926535 8979323846 2643383279...

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