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summation

Summation

means to sum the results of a formula for all values given

Basic example

i=14i2=12+22+32+42=30

Simplification

Distributive property

a(b+c)=ab+ac

In other words, constants inside the summed expression can be pulled outside.

Example

i=14i2=30=i=143i2=3(12)+3(22)+3(32)+3(42)=3[12+22+32+42]=3[i=14i2]

Distributive property

a+b=b+a

In other words we can add the terms in any order

Example

i=14(i2+2i)=(12+2(1))+(22+2(2))+(32+2(3))+(42+2(4))=(12+22+32+42)+(2(1))+2(2))+2(3))+2(4)) =i=14i2+i=142i

Summation of constants

When summing constants, you can multiply the constant by the number of indices you count.

Example

k=1105=5+5+5+5+5+5+5+5+5+5=105=50

See also

Mean and Variance

Based on course material by Paul Bendich and Daniel Egger from Data Science Maths Skills