Math, asked by harshinidass88, 6 months ago

find the mean of squares of first n natural numbers ​

Answers

Answered by shashiprabha1681
1

Step-by-step explanation:

The average of squares of first n natural numbers = (n+1)(2n+1)/6. The average of cubes of first n natural numbers = n(n+1)2/4. ... The average of even numbers from 1 to n = (last even number+2)/2. The average of squares of first n odd numbers = (2n+1)(2n-1)/3.

I hope these will work for you

Answered by cy163279
1

The first n natural numbers are 1,2,3,...,n

Sum of squares of n natural numbers is 1

2

+2

2

+3

2

+...+n

2

We know that sum of squares of first n natural numbers is given by

6

n(n+1)(2n+1)

Mean is the average of the values of the data set.

Therefore, mean of the squares of first n natural numbers is

n

1

2

+2

2

+3

2

+...+n

2

=

6n

n(n+1)(2n+1)

=

6

(n+1)(2n+1)

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