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**

**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

How do you simplify

Offline

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

19CK is the short way of saying:

And you can write 19C(k+1) in a similar way.

Therefore, the fraction in the question is:

When you also expand out all the factorials (eg. k! = 1x2x3x4x5x...xk), then a lot of things can cancel out and leave you with something relatively simple.

The final answer is:

Why did the vector cross the road?

It wanted to be normal.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi 1a2b3c2212;

Divide top and bottom by 19!

Make use of the identity:

So 2) becomes:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

Is this correct?

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi 1a2b3c2212;

To prove a conjecture no amount of numerical evidence will suffice, but to disprove one you only need a single counter example.

So numerical experimentation ( plugging in numbers ) can be a powerful technique when trying to disprove something.

No it is not true, try the triplet ( n = 10 , k = 3 , r = 2 ) or an easier one to compute ( n = 7, k = 5 , r = 2 ).

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

Pages: **1**