Problem 6

Sum Square Difference

The sum of the squares of the first ten natural numbers is,

$1^{2} + 2^{2} + \dots + 10^{2} = 385$

The square of the sum of the first ten natural numbers is,

$(1 + 2 + \dots + 10)^{2} = 55^{2} = 3025$

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is $3025 - 385 = 2640$ .

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

前十个自然数的平方的和是

$1^{2} + 2^{2} + \dots + 10^{2} = 385$

前十个自然数的和的平方是

$(1 + 2 + \dots + 10)^{2} = 55^{2} = 3025$

因此，前十个自然数的平方和与和平方之差是 $3025 - 385 = 2640$ 。

求前一百个自然数的平方的与和平方之差。

译注：注意此处出题人使用的自然数定义不包含 $0$ 。