Problem 6

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

1² + 2² + … + 10² = 385

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

(1 + 2 + … + 10)² = 55² = 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.

Solution

— The sum of the squares of

— the first ten natural numbers is,

 

— 1^2 + 2^2 + … + 10^2 = 385

— The square of the sum of the

— first ten natural numbers is,

 

— (1 + 2 + … + 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.

 

select power(sum(number),2) – sum([square])

from Number

where number <= 100

 

Discussion

Just like the other solutions, this one is quite simple.  It is aided by the fact that when I populated my database I included all of the squares in the number table as well.

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).