8 ms·
That's a neat visualisation. n^2 = sum(1..n) - sum(1..n-1) = 2sum(1..n-1) + n => n^2 - n = 2sum(1..n-1) => n(n-1) = 2*sum(1..n-1) => sum(1..n-1) = n(n-1)/
by tomfitz 9y ago
That's a neat visualisation.
n^2 = sum(1..n) - sum(1..n-1)
= 2sum(1..n-1) + n
=> n^2 - n = 2sum(1..n-1)
=> n(n-1) = 2*sum(1..n-1)
=> sum(1..n-1) = n(n-1)/2
And you can rewrite that as...
sum(1..n) = n(n+1)/2
- nhebb 9y agoThat's it! Makes me realize how rusty at math I've gotten. :/