 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/19/a/i/solution

For every integer

n \geq 1

sin ((2 n - 1) π) = 0

and

cos ((2 n - 3) π) = - 1

. Thus the summand simplifies to

2/ n

. The resulting series is twice the harmonic series, so it diverges to $+ \infty$ .

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