MathDB
sum 1/a_k a_{k+1}=(n-1)/a_1a_n

Source: Polish MO Finals 1962 p1

August 30, 2024
algebraArithmetic ProgressionSum

Problem Statement

Prove that if the numbers a1,a2,…,an a_1, a_2,\ldots, a_n (n n - natural number ≥2 \geq 2 ) form an arithmetic progression, and none of them is zero, then 1a1a2+1a2a3+…+1an−1an=n−1a1an.\frac{1}{a_1a_2} + \frac{1}{a_2a_3} + \ldots + \frac{1}{a_{n-1}a_n} = \frac{n-1}{a_1a_n}.
Back to ProblemsView on AoPS