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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