Math Is Fun Forum

Yusuke00

Member

Registered: 2013-11-19

Posts: 43

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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 (2013-11-24 06:28:02)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Yusuke00

Member

Registered: 2013-11-19

Posts: 43

Re: Mathematical proofs?

Interesting proof,i thought of a different one.

Nehushtan

Member

Registered: 2013-03-09

Posts: 957

Re: Mathematical proofs?

Let

.

For any

we have

Adding

to both sides gives

. As this is true for all

we have

Since we are given

we must have

i.e.

.

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Yusuke00

Member

Registered: 2013-11-19

Posts: 43

Re: Mathematical proofs?

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Mathematical proofs?

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

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Mathematical proofs?

hi Yusuke00

http://www.mathisfunforum.com/viewtopic.php?id=4397

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob