Sum of square of n natural numbers
here lower limit is 1 and upper limit is 10 .
That means sum of squares of n natural numbers ranging from 1 to 10 can be calculated as
\[\sum_{1}^{10} n^{2} = \frac{n(n+1)(2n+1)}{6} = 385\]
Similarly \[\sum_{1}^{100}n^{2} \]= 338350 and so on.
Hence 12 + 22 + 32 + 42 + ........................ + n 2 can be easily calculated using above formula.
where must belongs to some integer
