TNPSC – AVERAGE

TNPSC – AVERAGE

Average:

=> The average of first n natural numbers = (n+1)/2

=> The average of the first n consecutive even numbers = (n+1)

=> The average of the first n consecutive odd numbers = n

=> The average of the first n odd natural numbers = (Last odd number+1) / 2=> The average of the first n even numbers = (Last even number+1) / 2

=> The average of the squares of the first n natural numbers can be shown to be (1/6) (n+1) (2n+1)

=> The average of the squares of the first n even natural numbers [2 (n+1) (2n+1)] / 3

=> The average of the squares of the first n odd natural numbers {(2n-1) (2n+1)] / 3

=> The average of the cubes of the first n natural numbers = [n (n+1)²] / 4