The mean of the following data 12,22,32,42,........n2 is
The sum of the squares of the first n natural numbers is n(n+1)(2n+1)6. The mean is the sum divided by the number of terms. Therefore, the mean is
n(n+1)(2n+1)6n=(n+1)(2n+1)6
Find the sum of 1.n2+2(n−1)2+3(n−2)2+......n.12
1.3+3.5+5.7+....+(2n−1)(2n+1)=n(4n2+6n−1)6
1.3+3.5+5.7+⋯+(2n−1)(2n+1)=n(4n2+6n−1)3.