Find a formula for... (Induction and Recursion)

Question

a)Find a formula for

$$\frac 1 2 + \frac 1 4 + \frac 1 8 + \cdots + \frac1{2^n}$$

by examining the values of this expression for small values of $n$.

b) Prove the formula you conjectured in part a.

If you can help me with part a, I would really appreciate it. I know how to prove it. I just can't find a formula to the first question.

Thanks.

You should have included the result of "examining the values of this expression for small values of $n$", which I assume is something you've done already. — , Oct 16 '14 at 02:32

Brian M. Scott · Accepted Answer · 2014-10-18T18:16:06.307

2

HINT:

$$\begin{align*} \frac12&=\frac12=1-\frac12\\ \frac12+\frac14&=\frac34=1-\frac14\\ \frac12+\frac14+\frac18&=\frac78=1-\frac18 \end{align*}$$

edited Oct 18 '14 at 18:16

answered Oct 16 '14 at 02:16

Brian M. Scott

There's a typo in the very first equality. – Git Gud Oct 18 '14 at 12:36
@GitGud: Thanks; fixed. (You were supposed to do a somersault while reading it!) – Brian M. Scott Oct 18 '14 at 18:16
Ahahah, good one. – Git Gud Oct 18 '14 at 22:51

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