Non-Consecutive Sequence

Hard

Probability

Suppose that you flip a coin

n

times and it turns out that no consecutive heads appear in the sequence. Let

E(n)

be the expected number of heads that appear given this information. Compute

\displaystyle \lim_{n \rightarrow \infty} \dfrac{E(n)}{n}

. The answer is in the form

\dfrac{a}{b + \sqrt{c}}

for integers

a,b,

and

c

with

c

minimal. Find

abc

Notes

Hint

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Question Contribution

Non-Consecutive Sequence

Hard

Probability

Suppose that you flip a coin

n

times and it turns out that no consecutive heads appear in the sequence. Let

E(n)

be the expected number of heads that appear given this information. Compute

\displaystyle \lim_{n \rightarrow \infty} \dfrac{E(n)}{n}

. The answer is in the form

\dfrac{a}{b + \sqrt{c}}

for integers

a,b,

and

c

with

c

minimal. Find

abc

Notes

Hint