 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/4/solution

a

r

with

∣ r ∣ < 1

, the sum is

a / (1 - r)

. Taking the initial term to be

2

gives

2 + 1 + \frac{1}{2} + \frac{1}{4} + \dots = \frac{2}{1 - 1/2} = 4,

and

2 - 1 + \frac{1}{2} - \frac{1}{4} + \dots = \frac{2}{1 + 1/2} = \frac{4}{3} .

1/2

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