Summary The notation with ∑

The notation with ∑

A sum can be written as follows, if N ≥M


∑


Which is read “sum of the terms ak when the value of k goes from M to N”. In this
context, ∑ is called the summation sign and k is known as the index of the sum.

Summation Notation Properties

Let {an} and {bn} be two real sequences and c be a real number. Then:


∑ ∑



∑( ) ∑ ∑



∑( ) ∑ ∑



∑ ∑ ∑

, Example #1. Interpretation of summation notation

Develop the following sum:


∑


Starting with k=1 and ending with k=5 we get:


∑


Example #2. Interpretation of summation notation

Develop the following sum:


∑


Starting with k=3 and ending with k=6 we get


∑


Example #3. Interpretation of summation notation

Develop the following sum:


∑


In this case ak=k2 y k goes from -2 to 3


∑ ( ) ( ) ( ) ( ) ( ) ( )




∑