Seems trivial. Pair them, each pair is worth -1.
f(1000) = 1 - 2 + 3 - 4 + ... + 999 - 1000
= (1 - 2) + (3 - 4) + ... + (999 - 1000)
= -1 -1 + ... + -1
= -500
Odd n left as exercise for the reader.
(I wrote this when the question title still said "1 − 2 + 3 − 4 + · · ·", can't be bothered to switch all signs now.)
Seems trivial. Pair them, each pair is worth -1.
f(1000) = 1 - 2 + 3 - 4 + ... + 999 - 1000
= (1 - 2) + (3 - 4) + ... + (999 - 1000)
= -1 -1 + ... + -1
= -500
Odd n left as exercise for the reader.
Seems trivial. Pair them, each pair is worth -1.
f(1000) = 1 - 2 + 3 - 4 + ... + 999 - 1000
= (1 - 2) + (3 - 4) + ... + (999 - 1000)
= -1 -1 + ... + -1
= -500
Odd n left as exercise for the reader.
(I wrote this when the question title still said "1 − 2 + 3 − 4 + · · ·", can't be bothered to switch all signs now.)
Seems trivial. Pair them, each pair is worth -1.
f(1000) = 1 - 2 + 3 - 4 + ... + 999 - 1000
= (1 - 2) + (3 - 4) + ... + (999 - 1000)
= -1 -1 + ... + -1
= -500
Odd n left as exercise for the reader.
default