MathDB
2018 PUMaC Live Round 1.3

Source:

January 13, 2019
PuMACLive Roundprobabilityexpected value

Problem Statement

Let a sequence be defined as follows: a0=1a_0=1, and for n>0n>0, ana_n is 13an−1\tfrac{1}{3}a_{n-1} and is 19an−1\tfrac{1}{9}a_{n-1} with probability 12\tfrac{1}{2}. If the expected value of ∑n=0∞an\textstyle\sum_{n=0}^{\infty}a_n can be expressed in simplest form as pq\tfrac{p}{q}, what is p+qp+q?
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