Re: what math rule is this?
- From: José Carlos Santos <jcsantos@xxxxxxxx>
- Date: Tue, 07 Mar 2006 09:25:18 +0000
On 07-03-2006 9:15, Foster Bell wrote:
Our discrete math textbook mentions in passing that 2^(ab-1) = (2^a -
1) * (2^(a*(b-1)) + 2^(a * (b-2)) + ... + 2^a + 1).
I don't remember seeing this before. What's it called?
If you put 2^(a*b) - 1 instead of 2^(a*b - 1) (which leads to a false
equality), it's called "sum of a geometric progression":
2^(a*(b - 1)) + 2^(a*(b - 2)) + ... + 2^a + 1 =
= (2^a)^(b - 1) + (2^a)^(b - 2) + ... + (2^a)^1 + (2^a)^0
= ((2^a)^b -1)/(2^a - 1)
= (2^(a*b) -1)/(2^a - 1).
Best regards,
Jose Carlos Santos
.
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