Problem

Source: Bosnia and Herzegovina TST 2014 day 2 problem 1

Tags: algebra solved, algebra



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.