Question

The mean of the sauare of the first 'n' natural is.​

Answer 1

The mean of a set of values is equal to the sum of all the values divided by the number of values. The sum of the first natural numbers is n ( n + 1 ) 2 . This is a well-known result and it's worth memorising. Therefore the mean of the first natural numbers is n + 1 2 .

Answer 2

As you know,

Sum of the squares of n natural numbers can be found by a formulae :

S = n*(n+1)*(2n+1)/6

So, average of sum of squares of first n natural numbers will be :

Average = (Sum of squares of n natural numbers) / (n)

But, in the question, it is asked for 2m natural numbers.

So, replace 'n' with '2m'.

We get,

AVERAGE = {m*(m+1)*(2m+1)/6 } /2m

∴ AVERAGE = (m+1)*(2m+1)/12