 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/5/e/ii/solution

Using the differentiated geometric series,

S_{A B} = 2 p n = 1 \sum \infty n q^{n - 1} = \frac{2 p}{( 1 - q ) ^{2}} = \frac{2}{p} .

This is finite for

p > 0

, equals two when every visit succeeds, and diverges as the chance of success tends to zero.

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