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Write the following sequence as a recurrence relation (with sufficient initial values specified):

$b_n=1-\frac{1}{2^n} \forall n\in\mathbb{N}^*$

I think I am suppose to use induction (e.g. n-1) to prove the recurrence, but I am confused, how?

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    So what is $b_n - b_{n-1}$? What is $b_1$ or $b_0$?2011-02-17

2 Answers 2

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HINT $\ $ Eliminate $\rm\ 1/2^n\ $ from the equations for $\rm\ b_n,\ b_{n+1}\ $

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If you wrote $\frac{1}{2^{n}} = 1 - b_{n}$ and similarly for the $n-1$ case then you could probably see a relationship between $b_{n-1}$ and $b_n$