The sum of the first n positive integers is 31375. Determine the value of n.
2006-06-14 13:51:29 · 5 answers · asked by Miranda J 1 in Science & Mathematics ➔ Mathematics
n(n+1)/2 = 31375
n^2 + n = 62750
n^2 + n - 62750 = 0
n = (-1 +- sqrt(1^2 +4*1*62750))/2
= (-1 +- 501)2
so n = -502/2 = -251 or n = 500/2 = 250
Since you are talking about positive integers, n = 250.
edit: dewcoons, not that I'm offended or anything, but how is this "cheating"? I think this is the most straight forward way of answering the question.
2006-06-14 13:57:48 · answer #1 · answered by blahb31 6 · 1⤊ 0⤋
What the question is ask is: if you took all the positive intergers (non-fractions) and multipied them together, how many would have to multiple to get 31375.
So:
1*2=2
1*2*3=6
1*2*3*4=24
....
keep going until you get =3137
Then count up how many numbers you had to multiple. (Will be the same as the last number) That will be n.
You are on your own from there.
(Now that you understand the questionj, you can "cheat" and use the formula n(n+1)/2=3137 to get it quicker)
2006-06-14 20:59:47 · answer #2 · answered by dewcoons 7 · 0⤊ 0⤋
250?
2006-06-14 20:56:36 · answer #3 · answered by AJ 2 · 0⤊ 0⤋
too compicated for me to write down for you but it is 250
2006-06-14 22:27:07 · answer #4 · answered by coolpowwow80 3 · 0⤊ 0⤋
12.75
2006-06-14 20:55:12 · answer #5 · answered by smart_twin06 3 · 0⤊ 0⤋