MathDB

Easy sequence

Source: Bosnia and Herzegovina TST 2014 day 2 problem 1

May 11, 2014

algebra solvedalgebra

Problem Statement

Sequence

a_n

is defined by

a_1=\frac{1}{2}

a_m=\frac{a_{m-1}}{2m \cdot a_{m-1} + 1}

for

m>1

. Determine value of

a_1+a_2+...+a_k

in terms of

k

, where

k

is positive integer.