My professor gave an example located on slide 3 of this pdf: can anybody explain to me how he ended up with m_n = 2^(n) – 1. Thanks!
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My professor gave an example located on slide 3 of this pdf: can anybody explain to me how he ended up with m_n = 2^(n) – 1. Thanks!
The step is from
mn =2n−1 +2n−2 +…+22 +2+1.
to
mn = 2n − 1
There are two ways to make the step. One is to recognize this as a geometric series, and know the rule:
sum=(1-rn)/(1-r)
The other is to have played around enough with powers of two to know that if you add up a bunch of them starting from 1, you get the next one, minus one.