Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,334

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.

Offline

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?

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

Offline

**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,334

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.

Offline

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**

Offline

Pages: **1**