# Euler 0006

### The Problem:

The sum of squares n is defined by the sum of natural numbers ascending, such that, sum\_of\_squares(10) is 385. 1^2 + 2^2 + ... 10 ^2.   
The square of sum n is defined by the square of the sum of natural numbers ascending, such that, square\_of\_sum(10) is 3025. (1+2+...+10)^2 = 3025  
**Find the difference of these 2 values where n is 100.**

### Considerations:

Funny enough, this doesn't even need iterative computation, there are 2 different formula we can work with:  
\- Sum of square: n(n+1)(2n+1)/6  
\- Sum of numbers (and then squared): (n(n+1)/2)^2

### The Solution (No-Code!):

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Which means that the final formula is (n(n+1)/2)^2 - n(n+1)(2n+1)/6  
Which by hand:  
\- (100(101)/2)^2 - 100(101)(201)/6  
\- 25502500 - 338350  
\- 25164150

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