 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2001/paper-1/9/a/solution

Integrate the geometric series for

1/ (1 + x)

from zero to

x

. The first three nonzero terms are

ln (1 + x) = x - \frac{x ^{2}}{2} + \frac{x ^{3}}{3} + O (x^{4}) .

The resulting Taylor series converges for

∣ x ∣ < 1

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