Basic Summation Rules

n - is a variable which represents a whole number

                  Rule                                                   Example

  n

  E  k     k = n(n+1)

k = 1                2

  5

  E  k       k = 5(5+1)  = 15

 k = 1                2

  n

  E k²     k = n(n+1)(2n+1)

k = 1                  6

  6

  E k²       k = 6(7)(13)  = 91

 k = 1                  6

  n

  E  k³    k = ((n(n+1))/2)²

k = 1n            

  4

  E  k³      k = ((4(5))/2)²   =  100 

 k = 1

  n

  E  C     k = C*n

k = 1

  5

  E  4       k = 4*5  = 20 

 k =1

 

For Riemann Sums and Trapezoid Rule simply use the calculator located at the bottom of this page.

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