MathDB

21

Part of 2003 Purple Comet Problems

Problems(1)

Problem 21, Fall 2003 , MS and HS

Source:

6/23/2011
Let an=1+(1−1n)2+1+(1+1n)2,n≥1a_n = \sqrt{1 + (1 - \tfrac{1}{n})^2} + \sqrt{1 + (1 + \tfrac{1}{n})^2}, n \ge 1. Evaluate 1a1+1a2+…+1a20\tfrac{1}{a_1} + \tfrac{1}{a_2} + \ldots + \tfrac{1}{a_{20}}.