Math and science::Analysis::Tao::07. Series

Finite series, definition

Let

m, n

be integers, and let

(a_{i})_{i = n}^{m}

be a finite sequence of real numbers, assigning a real number

a_{i}

for each integer

i

between

n

and

m

inclusive (i.e.

m \leq i \leq n

). Then we define the finite sum (or finite series)

\sum_{i = m}^{n} a_{i}

by the recursive formula

\begin{aligned} \sum_{i = m}^{n} a_{i} & = 0 whenever n < m; \\ \sum_{i = m}^{n + 1} a_{i} & = [. . .] whenever [. . .] . \end{aligned}

15.11.2019