Correct solutions came from Bradley University community member Scott Small. Other correct solutions were submitted by Iñigo Picaza, Bill Webb, Gary Smith, Lisa Schechner, Larry Bell, Paul Botham, Juan Carlos Marivela, Dan Dima, Aaron Kahn, and, of course, the proposer, Lou Cairoli.

The first few partial sums are 1/2, 5/6, 41/42, 1805/1806.  The first few terms suggest a general pattern:  1/p₀ + 1/p₁ + ... + 1/p_n = 1 - 1/(p_n+1 - 1); this is, in fact, easy to prove by induction.   Since p_n ® 0 as n ® _, the series converges to 1. 

You are visitor number 2646 to this page.
©2005 Alberto L. Delgado