Monday

August 29, 2016
Posted by **please help me out!!!!** on Monday, February 18, 2013 at 12:56am.

- geometry!!! -
**Reiny**, Monday, February 18, 2013 at 1:08amDo you mean the largest "triangular number" ?

Triangular numbers are

1 , 3, 6, 10, 15, 21 , ....., n(n+1)/2

so n(n+1)/2 ≤ 1000

n^2 + n ≤ 2000

n^2 + n - 2000 ≤ 0

let's solve the equation

n = (-1 ± √8001)/2 = appr 44.2 or a silly negative

if n = 44 , term(44) = 44(45)/2 = 990

if n = 45 , term (45) = 45(46)/2 = 1035 too big

the largest triangular number < 1000 is 990