This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: -2 n n h). X n =1 n (ln n ) n Bonus: Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula 1 = 2 2 9801 X n =0 (4 n )!(1103 + 26390 n ) ( n !) 4 396 4 n William Gosper used this series in 1985 to compute the rst 17 million digits of . (a) Verify, by hand, that the series is convergent. (b) How many correct decimal places of do you get if you use just the rst term of the series? What if you use two terms? (c) What is the smallest number of terms you need to use in order to guarantee that you get the rst 100 decimals of ? (Hint: For b and c it would be wise to use a computer program, say mathematica.) 2...
View Full Document
- Spring '08