The sum of the squares of the first n natural numbers is given by n-n-1-2n-1-2-FalseTrue

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Standard X

Mathematics

Sum of Squares of n Natural Numbers

The sum of th...

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The sum of the squares of the first $n$ natural numbers is given by $\frac{n (n + 1) (2 n + 1)}{2} .$

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Question 87

The sum of squares of first n natural numbers is given by $\frac{1}{6} n (n + 1) (2 n + 1)$ or $\frac{1}{6} (2 n^{3} + 3 n^{2} + n)$ . Find the sum of squares of the first 10 natural numbers.

Prove that: 1 + 2 + 3 + ......... + n = $\frac{n (n + 1)}{2}$ i.e., the sum of the first n natural numbers is $\frac{n (n + 1)}{2}$ .

Q. 1 + 2 + 3 + ... + n =

\frac{n (n + 1)}{2}

i.e. the sum of the first n natural numbers is

\frac{n (n + 1)}{2}

The sum S of first n even natural numbers in given by the relation S = n(n + 1). Find n, if the sum is 420.

Q. Statement-1 : The variance of first n even natural numbers is

\frac{n^{2} - 1}{4}

Statement-2 : The sum of first n natural numbers is

\frac{n (n + 1)}{2}

and The sum of squares first n natural numbers is

\frac{n (n + 1) (2 n + 1)}{6}

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The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)2.

The sum of the squares of the first $n$ natural numbers is given by $\frac{n (n + 1) (2 n + 1)}{2} .$