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**

**hempy****Member**- Registered: 2012-11-06
- Posts: 2

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.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,654

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

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,654

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,796

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

For example a[sub]n[/sub].

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.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,650

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,796

Pretty math?

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.

Offline

**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

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.

Offline

Pages: **1**