# geometry!!!

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What is the largest triangle number that is less than 1000?

• geometry!!! -

Do 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

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