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Using the following formula for a triangular number, verify that 1225 and 41 616 are triangular numbers. [Hint verify that there is an n for each number that satisfies the equation]

e.g., t5 = 15 =(5+1)/2
tn = n(n+1)/2

so, should I plug in 1225 and 41,616 and work the equation out? Somehow, I'm just reall confused by this problem. Could someone please be so kind as to help me?

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  1. no, find n for each. I will do one.

    41,616= n(n+1)/2
    83,232= n^2+n

    put it in binomial form, and solve

    n^2+n-83232=0

    n= (-1+-sqrt 332929)/2= -1/2 +-288.5
    n= 288, or n=-289

    Now put them in the formula and verify. Normally, we restrict n to positive values, but your problem did not.

    Now do the other number.

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    bobpursley
  2. oh, okay! I'll try it out; thanks so much!

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  3. sorry, but I don't get where you're getting "n= (-1+-sqrt 332929)/2= -1/2 +-288.5" could you please explain?

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  4. 1) I made an error in the next to last line.
    n=0,180,360....the 1 was a typo.

    Now, how did I get n. It came from the binomial equation for the quadratic form

    if

    ax^2+bx + c=0, then

    x= (-b+-sqrt(b^2-4ac))/2a

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    bobpursley
  5. oh... okay, thanks for the correction and the explanation

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