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JH

# Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula $\frac {1}{\pi} = \frac {2 \sqrt{2}}{9801} \displaystyle \sum_{n = 0}^{\infty} \frac {(4n)!(1103 + 26390n)}{(n!)^4396^{4n}}$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?

## a. convergent.b 6 decimal places; 15 decimal places

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