MathDB

28

Part of 2013 Harvard-MIT Mathematics Tournament

Problems(1)

2013 HMMT Guts #28: Sum of Sums of Series

Source:

3/26/2013
Let z0+z1+z2+⋯z_0+z_1+z_2+\cdots be an infinite complex geometric series such that z0=1z_0=1 and z2013=120132013z_{2013}=\dfrac 1{2013^{2013}}. Find the sum of all possible sums of this series.
HMMTratiogeometric series