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![Page 1: 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 = 1 + 2 +](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d845503460f94a6b1fe/html5/thumbnails/1.jpg)
Special Sum
The First N Integers
![Page 2: 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 = 1 + 2 +](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d845503460f94a6b1fe/html5/thumbnails/2.jpg)
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
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
![Page 3: 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 = 1 + 2 +](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d845503460f94a6b1fe/html5/thumbnails/3.jpg)
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
![Page 4: 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 = 1 + 2 +](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d845503460f94a6b1fe/html5/thumbnails/4.jpg)
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)
225 + 5
2= 15=
![Page 5: 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 = 1 + 2 +](https://reader036.vdocument.in/reader036/viewer/2022082816/56649d845503460f94a6b1fe/html5/thumbnails/5.jpg)
9/9/2013 Sum of 1st N Integers 5
Think about it !