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Re: induction question
Posted:
Feb 27, 2007 9:50 AM
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On Feb 27, 2007 1:44 AM CT, Earth wrote:
> 1+2+3+...+n =n(n+1)/2
> conclusion
> (n-1)n/2+n = n(n+1)/2
For this one you're asked to prove that
1 + 2 + ... + n = n(n + 1) / 2
...via induction. This is a formula - it gives us the
value of the summation of the first n integers as a
product.
It seems you know how to do this. First, you show that
the formula is true for the first few n (n = 1, 2, etc).
Then you assume that it is true for n = k (our induction
hypothesis), and proceed to show that it is true for n =
k + 1.
> a)what would be the last step in a similar inductive
> proof that
> n(1/1! + 1/2! +...+(-1)^n/n!)?
> what is the conclusion on this? how do work on it to
> get answer?
This, on the other hand, is not a formula nor an
equation for anything.
It is an expression - you cannot prove an expression.
Regards,
Kyle Czarnecki
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