Very Heavy Coin

Calculus Level 5

You are flipping a coin that has a \(\dfrac{n^2-1}{n^2}\) chance of landing on heads. The value of \(n\) follows these rules:

  • \(n\) and \(k\) initially equal 2.

  • Whenever the coin lands on heads, \(n\) increases by 1.

  • Whenever the coin lands on tails, \(k\) increases by one and then \(n\) is set to equal \(k\) (e.g. the first time you flip tails, \(k\) and \(n\) will both equal 3, then the second time they will equal 4, etc.)

What is the average number of tails you will flip?

Give your answer to 3 decimal places.


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