1. Special Sum The First N Integers

2. 9/9/2013 Sum of 1st N Integers 2 Sum of the First n Natural Numbers Consider Summation Notation ∑ k=1 n k = 1 + 2 + 3 + … + (n – 2) + (n – 1) + n Add OR =n + (n – 1) + (n – 2) + … + 3 + 2 + 1 ∑ k=1 n k ∑ n k2 = (n + 1) + (n + 1) + (n + 1) + … + (n + 1) giving

3. 9/9/2013 Sum of 1st N Integers 3 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

4. 9/9/2013 Sum of 1st N Integers 4 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) 2 25 + 5 2 = 15 =

5. 9/9/2013 Sum of 1st N Integers 5 Think about it !