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# Exponent Result Watch

1. Is there a result proving/stating that:
2^n > 2^(n-1) - 2^(n-2) - ... - 2 - 1 for n > 0
2. (Original post by md100)
Is there a result proving/stating that:
2^n > 2^(n-1) - 2^(n-2) - ... - 2 - 1 for n > 0
Do you think negative powers on the right side?
If Yes
2^n > 2^(n-1) > 2^(n-1)-2^(n-2)- ...
3. (Original post by md100)
Is there a result proving/stating that:
2^n > 2^(n-1) - 2^(n-2) - ... - 2 - 1 for n > 0
Obvously 2^n > 2^(n-1) and your right hand side is less than 2^(n-1) so your inequality is true.

Did you mean 2^n > 2^(n-1)+2^(n-2).....+2+1 ?

This is also true.

16>8+4+2+1=15

32>16+8+4+2+1=31

You could use the formula for a geomtric series.
4. My bad. Ye I meant plus. Cheers. Just wondering if there is a result I could use to show this. And the fact that

1^n < 1^n-1 + 1^n-2 ............. + 1.

I know its obvious. Not sure if I would need to state it as a result though.

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Updated: December 21, 2010
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