MathDB

A robot on the number line starts at

1

. During the first minute, the robot writes down the number

1

. Each minute thereafter, it moves by one, either left or right, with equal probability. It then multiplies the last number it wrote by

n/t

, where

n

is the number it just moved to, and

t

is the number of minutes elapsed. It then writes this number down. For example, if the robot moves right during the second minute, it would write down

2/2=1

.
Find the expected sum of all numbers it writes down, given that it is finite.
Proposed by Ethan Tan

Problem Statement