Calculus Student
Franklin & Marshall College
Lancaster, PA 17604
Dear Calculus Student:
We at SILU have had an exciting new development and we are anxiously hoping that you can help us. Your enthusiastic professor, Dr. Crannell, assured us that you'd be more than willing.
About a week ago, we pointed our telescope towards a region of space near Tau Ceti and picked up a strong signal, a signal we'd never heard before. Although the signal is seemingly random, we have reason to believe that it comes from an intelligent life which is trying desperately to communicate with us.
Our guess is that the signal is either the decimal expansion of  or else of e . If so, then our search for intelligent life is over, because no known natural phenomena can produce such a sequence. Our problem is that we don't know how long the signal has been broadcasting, and so we need to find a way to calculate both e and to many decimal places. We had a pair of resident mathematicians working on it, but they were so overcome by the excitement and caffeine that they began babbling, "Drink up, E.T.", and we sent them away for some rest.
On their desk, we found the following. We don't know if it will help you or not.
We don't know if this is enough information for you to piece together a good pair of formulas, but we certainly hope so. We would also appreciate your demonstrating the formulas to us and getting both and e to 5 decimal places. If possible, we would like an answer by February 11, 1993.
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