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authormo khan <mo@mokhan.ca>2021-09-19 15:50:44 -0600
committermo khan <mo@mokhan.ca>2021-09-19 15:50:44 -0600
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learn about sigma notation and arithmetic summations
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+[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
+-------
+```