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## #1 2012-11-07 17:07:42

hempy
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### Induction Proofs

Let a(sub0) and r be fixed real numbers with r ≠ 0 and r ≠ 1, and suppose that for each n ∈ N, a(subn) = r*a(subn-1).

For every nonnegative integer n, a(subn) = a(sub0) * r^n.

Prove by induction.

## #2 2012-11-07 18:53:11

bob bundy
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### Re: Induction Proofs

hi hempy,

The following site has an explanation of proof by induction.  The final example is the proof for the geometric sequence.  The notation is a little different but you should be able to 'convert it'.

http://www.csee.umbc.edu/~stephens/203/PDF/4-2.pdf

Bob

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

## #3 2012-11-08 18:22:40

noelevans
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### Re: Induction Proofs

Hi!

Suppose that a   is a constant and r is not zero or one and for each n in {1,2,3,...}
0
n
a   = r*a     .    Show that a  = a * r    for each n in {1,2,3,...}.
n         n-1                      n     0
1
For n=1 we have a  = r*a     = r*a  = a *1  .   So it works for n=1.
1        1-1        0     0

Now suppose that for some positive integer k,

k                                                               k               k          k+1
we have a  = a *r  .   Then  a      = r*a           = r*a   = r*a *r  = a * r * r   = a*r
k     0                   k+1        (k+1)-1        k         0         0                0

So given that it works for k we have shown that it works for k+1, which is the inductions step.
Therefore it works for all n in {1,2,3,...}.

Is there any way to put this page into a half-space mode?  Then the super and subscripts would
look pretty nice.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

## #4 2012-11-08 19:21:42

bob bundy
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### Re: Induction Proofs

hi noelevans

You could try Latex:

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

Bob

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

## #5 2012-11-09 00:33:33

anonimnystefy
Real Member

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### Re: Induction Proofs

The forum also has built in tags which allows use of subscripts and superscripts withouth knowledge of latex:

For example an.

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

## #6 2012-11-09 03:47:16

bobbym

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### Re: Induction Proofs

Hi noelevans;

Give this a try:

http://latex.codecogs.com/editor.php

perfect latex everytime!

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #7 2012-11-09 06:25:25

noelevans
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### Re: Induction Proofs

Thanks all!

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

## #8 2012-11-09 07:25:50

anonimnystefy
Real Member

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### Re: Induction Proofs

Pretty math?

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

## #9 2012-11-09 12:29:58

noelevans
Full Member

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### Re: Induction Proofs

LaTex input (not so pretty) vs LaTex output = Pretty math

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.