We are given the formula for the sum of the first n positive integers, and we are asked to find n when this formula gives a sum of 666.
1/2n(n+1)=666
We can solve this quadratic equation in two steps.
First let's rearrange it to standard form, then let's use the Quadratic Formula to find the solution.
Once we have the equation in standard form, we can use the Quadratic Formula to solve it.
2
&Quadratic equation: && ax^2+ bx+ c=0
&Solutions:&&x=- b±sqrt(b^2-4 a c)/2 a
Let's identify the coefficients in our quadratic expression.
n^2+n-1332= 1n^2+ 1n+( - 1332)
We see that a= 1, b= 1, and c= -1332. Let's substitute these values into the Quadratic Formula.
Since we are looking for a positive integer, we only consider the solution with a sum in the numerator.
n=-1+73/2=72/2=36
We need to add 36 integers from 1 to 36 to get the sum 666.
