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

You are not logged in.

## #1 2013-11-25 05:14:18

Yusuke00
Member

Offline

### Mathematical proofs?

Hey guys.I just came out with a new problem i discovered.
Let it be n>=2 a natural number and n rational numbers with the property that,however we pick one of them,the sum of the other n-1 is 0.Show that all the numbers are equal to 0.
xD have fun

## #2 2013-11-25 05:27:46

anonimnystefy
Real Member

Offline

### Re: Mathematical proofs?

Let the numbers be

and
for
.

Then we have that
for
. We see that all of the numbers are the same. It is now obvious that they must all be zero.

Last edited by anonimnystefy (2013-11-25 05:28:02)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #3 2013-11-26 01:08:10

Yusuke00
Member

Offline

### Re: Mathematical proofs?

Interesting proof,i thought of a different one.

## #4 2013-11-26 02:04:28

Nehushtan
Power Member

Offline

### Re: Mathematical proofs?

Let
.

For any
we have

to both sides gives
. As this is true for all
we have

Since we are given
we must have
i.e.
.

## #5 2013-11-26 04:47:23

Yusuke00
Member

Offline

### Re: Mathematical proofs?

How do you write mathematical here?
I mean with all the symbols and etc.

## #6 2013-11-26 05:40:05

anonimnystefy
Real Member

Offline

### Re: Mathematical proofs?

Use (math)(/math), except that you put [ and ] instead of ( and ). This enables you to use LaTeX on the forum.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #7 2013-11-26 10:33:17

bob bundy
Moderator

Offline

### Re: Mathematical proofs?

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei