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Mathematical induction :

Posted June 16th, 2009 by alpha
in

Prove by mathematical induction:
$ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}........+\frac{1}{2^n }=1-\frac{1}{2^n } $

‹ Coordinate Geometry Mathematical induction : ›

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Doubt

On June 16th, 2009 alpha says:

Generally ,in the final step we prove the given statement[P(n)] for n=k+1.
In this case , I think, in last step the statement is to be made true by putting n=k+2[since n is an even number.]

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answer

On June 16th, 2009 Structure says:

$ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}........+\frac{1}{2^n }=1-\frac{1}{2^n } $
$ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}........+\frac{1}{2^n }+\frac{1}{2^n }=1 $
$ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}........+\frac{1}{2^n }+\frac{1}{2^{n+1} }+\frac{1}{2^{n+1} }=1 $
$ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}........+\frac{1}{2^n }+\frac{1}{2^{n+1} }=1-\frac{1}{2^{n+1} } $
There is no reason to think n is odd or even

~~THANK YOU ~~

On June 16th, 2009 alpha says:

````Maths````
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(((())))
///

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