Kiriti's sum

Probability Level 3

Consider the sequence {an} \{ a_n\} defined by a1=22013a_1 = 2^{2013} and the recurrence relation

1ak=1a1+1a2+1a3++1ak1 for k>1. \frac {1}{a_k} = \frac {1}{a_1} + \frac {1}{a_2} +\frac {1}{a_3}+ \cdots +\frac {1}{a_{k-1}} \mbox{ for } k>1.

What is the value of a2013a_{2013}?

This problem is posed by Kiriti M.

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