Special Sum

The First N Integers

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Sum of the First n Natural Numbers Consider

Summation Notation

∑k=1

n

k = 1 + 2 + 3 + … + (n – 2) + (n – 1) + n

AddOR

= n + (n – 1) + (n – 2) + … + 3 + 2 + 1∑k=1

n

k

∑ k=1

n

k2 = (n + 1) + (n + 1) + (n + 1) + … + (n + 1)

giving

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Sum of the First n Natural Numbers

resulting in

Summation Notation

∑ k=1

n

k2 = (n + 1) + (n + 1) + (n + 1) + … + (n + 1)

= n(n + 1)

k=1

n

∑

k =n(n + 1)

2

Thus

n terms

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Sum of the First n Natural Numbers

Summation Notation

k=1

n

∑

k =n(n + 1)

2

Example:

k=1

5

∑

k =5(5 + 1)

225 + 5

2= 15=

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Think about it !