Property challenge: The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6. For n = 5, the squares are 1, 4, 9, 16, 25. What is 1^2 + 2^2 + 3^2 + 4^2 + 5^2?

Question

Accepted Answer

55. Using n(n+1)(2n+1)/6 with n=5: 5 × 6 × 11/6 = 330/6 = 55. (Check: 1+4+9+16+25 = 55.)

Property challenge: The sum of the squares of the first $n$ natural numbers is given by $\frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ .
For $n = 5$ , the squares are 1, 4, 9, 16, 25.
What is $1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2}$ ?

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More Class 8 Properties of Square Numbers practice

Property challenge: The sum of the squares of the first n natural numbers is given by 6n(n+1)(2n+1)​.For n=5, the squares are 1, 4, 9, 16, 25.What is 12+22+32+42+52?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Properties of Square Numbers practice

Property challenge: The sum of the squares of the first $n$ natural numbers is given by $\frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ .
For $n = 5$ , the squares are 1, 4, 9, 16, 25.
What is $1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2}$ ?