 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2021/prelims/mathematics-ii/3/a/solution

\sum_{n = 1}^{\infty} a_{n}

converges if its partial sums

s_{N} = \sum_{n = 1}^{N} a_{n}

S

N \to \infty

; its sum is then

S

. It has absolute convergence if the series

\sum_{n = 1}^{\infty} ∣ a_{n} ∣

converges, where

∣ a_{n} ∣

is the absolute value of the term.

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