I was just wondering I solve the first 50 even numbers so it's $(50)(51)$ $=$ $2550$ while 50 first odd is $n^2$ so $2500$. In numbers 1-10 there are 5 odds and 5 evens so why are they not equal?
[Math] Why is it the sum of even numbers are higher than sum of odd numbers
algebra-precalculussequences-and-series
Best Answer
Every odd contributes one less than the even following it. So for example, $$2 + 4 + 6 + 8 + 10 = (1+1) + (3+1) + (5+1) + (7+1) + (9+1) = 1 + 3 + 5 + 7 + 9 + (1+1+1+1+1)$$ so as you can see the sum of the first 5 evens is 5 higher than the sum of the first 5 odds.