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Breaking The Summation Formula (Part 2)

 1. Sum of Odd numbers: 1+3+5+7+9+....+n =? where n is an odd number


Solve:
let, n = 3

list = 1+3+5 = 9 ; 3^2=9 or 3*3 = 9

let, n = 5
list = 1+3+5+7+9 = 25 ; 5^2 =25 or 5*5 =25


• so, summation of n odd numbers = n^2 = n*n


2.Sum of Even numbers: 2+4+6+8+10+....+n =? where n is an even number
Solve:
n=4, list = 2+4+6+8 = 20; sum = 4^2+4 = 20 or 4*5 =20
n=7, list = 2+4+6+8+10+12+14 = 56; sum = 7^2+7 = 56 or 7*8 = 56


• so, summation of n even numbers = n^2+n = n*(n+1)



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