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.
Usando del codice:
sum_of_squares_100_nums = sum([i^2 for i in 1:100])
square_of_sum_100_nums = sum([i for i in 1:100])^2
println(Int64(square_of_sum_100_nums-sum_of_squares_100_nums))25164150
Mentre affidandoci alle formule matematiche più o meno note
\[ \text{(sum of squares 1 to n)} = \sum_{i=1}^n i^2 = \dfrac{n(n+1)(2n+1)}{6} \] \[ \text{(sum 1 to n)} = \sum_{i=1}^n i = \dfrac{n(n+1)}{2} \]si ricava comunque la risposta:
f(n) = (n*(n+1)/2)^2 - n*(n+1)*(2n+1)/6
Int64(f(100))25164150