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Omni-MATH / The positive integer i is chosen at random such that the probability of a positive integer k being chosen is (3)/(2) times the probability of k+1 being chosen. What is the probabil…

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problem

The positive integer ii is chosen at random such that the probability of a positive integer kk being chosen is 32\frac{3}{2} times the probability of k+1k+1 being chosen. What is the probability that the ith i^{\text {th }} digit after the decimal point of the decimal expansion of 17\frac{1}{7} is a 2 ?
Plain-text mathematical notation (without MathML)
The positive integer i is chosen at random such that the probability of a positive integer k being chosen is (3)/(2) times the probability of k+1 being chosen. What is the probability that the i^(th ) digit after the decimal point of the decimal expansion of (1)/(7) is a 2 ?
Original LaTeX notation
The positive integer $i$ is chosen at random such that the probability of a positive integer $k$ being chosen is $\frac{3}{2}$ times the probability of $k+1$ being chosen. What is the probability that the $i^{\text {th }}$ digit after the decimal point of the decimal expansion of $\frac{1}{7}$ is a 2 ?

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Source and history

task_id
ce785451-6d6e-5667-a8fc-db9072ec51f4
task_key
test--ce785451-6d6e-5667-a8fc-db9072ec51f4
task_revision_id
1
config / split
/ test

Official source

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