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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,047

Determine the value of n if 1 + 3 + 6 + ... +

n(n - 1) = 364What I did:

I know that 1, 3, and 6 are the result of arithmetic series with the starting value 1 and the difference 2, thus that sum can be written as

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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Monox D. I-Fly wrote:

No: this is not an arithmetic series. The terms form the sequence of triangular numbers, whose nth term is (which you can also write as , though I prefer the former).You have been asked to find the value of such that That last term is the nth term of the sequence . Notice that if , then . Similarly taking gives you , and so on. So what you actually want to do is find the value of such that:I know that 1, 3, and 6 are the result of arithmetic series with the starting value 1 and the difference 2, thus that sum can be written as

+ + + ... + = 364.

Do you know how to do that?

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,047

Other than

, no.Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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Have you come across these formulae before?

If not, then one approach (which fits the title of the thread more accurately, I suppose) is to prove this result by induction:

and then once you have, set that equal to 364 and solve.

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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