 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-ii/1/b/i/solution

Choose the sequence

a_{n} = (- 1)^{n} (n \geq 1) .

Every even index is a peak of a sequence

(a_{n})

, since its value is

1

and all later values are at most

1

. Every odd index is a peak of a sequence

(- a_{n})

for the same reason. Both sets of indices are infinite.

 New to topics? Read the docs here!