I came up with this and want to prove it...

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I came up with this and want to prove it but I dont know how, any idea?

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>>7646074

Wouldn't it just be how you came up with it worked backward?

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[eqn]3 \sum_{x=0}^y 3^x = \sum_{x=1}^{y+1} 3^x = \sum_{x=0}^y 3^x + 3^{y+1} -1[/eqn]

Therefore

[eqn] 2 \sum_{x = 0}^y 3^x = 3^{y+1}-1[/eqn]

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>[math]y \in \mathbb{N}[/math]

>[math]y > 0[/math]

why...

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>>7646074

Use full induction

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Use transfinite induction.

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>>7646083

because [math] \mathbb{N} \neq \mathbb{N}^* [/math]

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Just think about it in base 3.

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>>7646092

The equation is still true for y=0.

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>>7646104

Also, you should probably sum from 0 to y, and drop the 1 on the right side, for sake of clarity

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>>7646074

prove the more general case

(x^(n+1)-1)/(x-1)=sum x^k from k=0 to n

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It's really basic number theory stuff, if its true. You just use x and y when you should use m and n becouse they represent integers.

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>>7646277

actually the base can be equal to any real number=/=1

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