Special Sum The First N Integers

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

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

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) = 15 =

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