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5. In the 1910's, the Indian mathematician Srinivasa Ramanujan discovered the formula V8 9801 k=1 (4k)!(1103 + 26390k) (k!)43964k (a) Approximate the series with only the k = 0 term and compare this with what your calculator tells you is the value of T. How many digits are correct? (b) Do the same using the k = 0 and k = 1 term. How many digits are now correct? (In fact, each term of this remarkable series increases the accuracy by 8 digits!) (c) Prove that this series converges.

5. In the 1910's, the Indian mathematician Srinivasa Ramanujan discovered the formula V8 9801 k=1 (4k)!(1103 + 26390k) (k!)43964k (a) Approximate the series with only the k = 0 term and compare this with what your calculator tells you is the value of T. How many digits are correct? (b) Do the same using the k = 0 and k = 1 term. How many digits are now correct? (In fact, each term of this remarkable series increases the accuracy by 8 digits!) (c) Prove that this series converges.

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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5. In the 1910's, the Indian mathematician Srinivasa Ramanujan discovered the formula V8 9801 k=1 (4k)!(1103 + 26390k) (k!)43964k (a) Approximate the series with only the k = 0 term and compare this with what your calculator tells you is the value of T. How many digits are correct? (b) Do the same using the k = 0 and k = 1 term. How many digits are now correct? (In fact, each term of this remarkable series increases the accuracy by 8 digits!) (c) Prove that this series converges.
Transcribed Image Text:5. In the 1910's, the Indian mathematician Srinivasa Ramanujan discovered the formula V8 9801 k=1 (4k)!(1103 + 26390k) (k!)43964k (a) Approximate the series with only the k = 0 term and compare this with what your calculator tells you is the value of T. How many digits are correct? (b) Do the same using the k = 0 and k = 1 term. How many digits are now correct? (In fact, each term of this remarkable series increases the accuracy by 8 digits!) (c) Prove that this series converges.
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