00:01
So in this problem, we're given the formula, s equals to n over 2 times n plus 1, and that tells us the sum of the first n natural numbers.
00:09
So we want to figure out, well, how many consecutive natural numbers, starting with 1, would reduce the sum of 253? well, to do this, we would substitute 253 in place of s, so that 253 equals n over 2 times n plus 1.
00:26
So now we just have to solve this equation for n.
00:28
So i'm going to distribute the n over 2 on the right hand side, so that will leave us with n squared over 2 plus n over 2.
00:37
Next, we're going to get rid of our fraction by multiplying each side of our equation by 2.
00:43
Well, 2 times 253 is 506.
00:47
2 times n squared over 2 is just n squared, and 2 times n over 2 is just n.
00:53
Well, as you can see, we have a quadratic equation.
00:56
So we're going to set this equal to 0 by subtracting 500.
00:59
From both sides.
01:02
So we'll have 0 equals n squared plus n minus 506...