Around 1910 , the Indian mathematician Srinivasa Ramanujan discovered the formula\[\frac{1}{\pi}-\frac{2 \sqrt{2}}{9801} \sum_{n=0}^{=} \frac{(4 n) !(1103+26390 n)}{(n !)^{4} 396^{4 n}}\]William Gosper used this series in 1985 to compute the first17 million digits of $\pi$(a) Verify that the series is convergent.(b) How many correct decimal places of $\pi$ do you get if you use just the first term of the series? What if you use two terms?

Around 1910 , the Indian mathematician Srinivasa Ramanujan discovered the formula\[\frac{1}{\pi}-\frac{2 \sqrt{2}}{9801} \sum_{n=0}^{=} \frac{(4 n) !(1103+26390 n)}{(n !)^{4} 396^{4 n}}\]William Gosper used this series in 1985 to compute the first17 million digits of $\pi$(a) Verify that the series is convergent.(b) How many correct decimal places of $\pi$ do you get if you use just the first term of the series? What if you use two terms?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.4: Series And Their Notations

Problem 54SE: Write 0.65 as an infinite geometric series using summation notation. Then use the formula for...

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