From 99b8e37803d8b64a0fb7d9a271e12bd02101a466 Mon Sep 17 00:00:00 2001 From: mo khan Date: Sun, 19 Sep 2021 15:50:44 -0600 Subject: learn about sigma notation and arithmetic summations --- math.md | 47 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 47 insertions(+) create mode 100644 math.md (limited to 'math.md') diff --git a/math.md b/math.md new file mode 100644 index 0000000..be7d56f --- /dev/null +++ b/math.md @@ -0,0 +1,47 @@ +[Σ Sigma notation](https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum) +Sum of some terms +Sum of the first 10 #'s + +``` +------- + 10 | | + Σ i | 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 | 55 + i=1 | | +------- + +------- + 100 | + Σ i | 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 .... 100 + i=1 | +------- + +sum := 0 +for i = 1; i <= 100; i++ { + sum += i +} + +``` + +The summation is an arithmetic series and has the value +``` +------- + n | | + Σ k | 1 + 2 + ... + n | + k=1 | | +------- +``` + +Sum of squares: +``` +------- + n | n(n+1)(2n+1) + Σ k^2 | = -------------- + k=0 | 6 +------- + +------- + n | n^2(n+1)^2 + Σ k^3 | = ------------- + k=0 | 4 +------- +``` -- cgit v1.2.3