Help with Mathematical Induction problems

emilyy

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Aug 24, 2014
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I need help for 2 mathematical induction proof problems:

1) Show that 1 + x + x2 + ... + xn = (1 - xn) / (1 - x)
where x∈R-{1} and n∈N

2) If A is a et with n elements, show that it has 2n subsets (including Ø and itself)


if you could help me I would really appreciate it!!! thank you :)
 
If you want help then tell us what help you need! Do you know what "proof by induction" is? Were you able to do the "first step"? What do you need to prove now?
 
If you want help then tell us what help you need! Do you know what "proof by induction" is? Were you able to do the "first step"? What do you need to prove now?
Well usually the first step is the basis step, which is prove with n=1, but in the first case I also have x, and I don't know what to do with it. How do I apply the basis step when I have n and also x ? I need to prove that it is true. And for the second one I just really don't get how to prove it!
 
Oh, c'mon! x is not a positive integer so "induction" must be "induction on n" and x just "goes along for the ride.

What is each side of the equation when n= 1?
 
Oh, c'mon! x is not a positive integer so "induction" must be "induction on n" and x just "goes along for the ride.

What is each side of the equation when n= 1?
1 + x + x2 + ... + x1= (1 - x1) / ( 1 - x)


??
sorry hehe I really have no clue what to do, I've had only one lesson on mathematical induction
 
1 + x + x2 + ... + x1= (1 - x1) / ( 1 - x)


??
sorry hehe I really have no clue what to do, I've had only one lesson on mathematical induction
(1 - x1) / ( 1 - x) = ?
 
1 + x + x2 + ... + x1= (1 - x1) / ( 1 - x)


??
sorry hehe I really have no clue what to do, I've had only one lesson on mathematical induction
It's not a matter or "mathematical induction", it is basic algebra and arithmetic. What is 2/2? What is 7/7? What is a/a for any number a?
(Is it the fact that you have "x1" in the numerator and "x" in the denominator? What is "x1?)
 
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