Skip to main content

average of first n natural numbers

By
The natural numbers are 1,2,3,4,5,. . . . . .
now we will see the sum of natural numbers
                      sum of first 3 natural numbers= 1+2+3=6
the above can be written as
                     sum of first 3 natural numbers= 1+2+3=6=3(3+1)/2
                     sum of first 4 natural numbers= 1+2+3+4=4(4+1)/2
                     then sum of n natural numbers=1+2+3+......n terms=n(n+1)/2

then the average formula = sum of elements/no of elements
                    the average of n natural numbers= sum of elements/ no of elements
                                                                        =(n(n+1)/2)/n
                                                                        =n(n+1)/2xn
                                                                        =(n+1)/2
 THE AVERAGE OF FIRST N NATURAL  NUMBERS=(n+1)/2

The average of first 5 natural numbers
                                 sum of 5 natural numbers=1+2+3+4+5=15
                                 no of elements = 5
                                 average = 15/5 =3

by formula  = average of first 5 natural numbers = (n+1)/2 =(5+1)/2
                                                                                              =6/2
                                                                                              =3

Comments

Post a Comment

Popular posts from this blog

pythagoras triangle numbers from difference between two adjacent numbers

By
1 2 =1x1=1                           ---->3 2 2 =2x2=4                           ---->5 3 2 =3x3=9                           ---->7 4 2 =4x4= 16                           ----> 9 --->(pythagoras numbers 16+9=25 ==>  4 2 +3 2   = 5 2 ) 5 2 =5x5= 25                           ---->11  6 2 =6x6=36            ...
Post a Comment
Read more

product two consecutive odd numbers

By
Product of two consecutive odd numbers : Even numbers are 1,3,5,7,9,11,13,15,17,19,21,23,25,..... Odd  number means when we divide a number with 2,then the remainder is equal to one. Difference between the two odd numbers is 1. Now we will discuss the product of two odd  numbers. Now the product of two even numbers assumed to be 5x7 can be written as (6-1)x(6+1).                              5x7= (6-1)x(6+1) From the above we write general formula as 5x7= (6-1)x(6+1)=6 2 -1 2  =36-1=35 Now we can observe the result as one less than the square number. So now we can observe the following table. Column 1&2 reprecent the adjacent odd numbers. Column 3 represent the product of two adjacent odd numbers. Column 4 represent  the nearest square number. This  will arrive by adding 1 to the product  of two odd ...
Post a Comment
Read more

Average of first n even numbers

By
Even numbers are 2,4,6,8,10,…. Average = sum of elements/ no of elments Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6= 2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) Now we will see average: Average of first 2 even numbers= (2+4)/2                                                           = 6/2                              ...
2 comments
Read more