# Induction - prove in induction on n that n/2^n < 2

### Induction - prove in induction on n that n/2^n < 2

hi

i did only that a5=114 but the else i try so hard and didnt success

help me plz

thx
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### Re: Induction - prove in induction on n that n/2^n < 2

"Induction" is pretty standardized! You want to use "proof by induction" to prove that $$\frac{n}{2^n}< 2$$ for n any positive integer. When n= 1 that says $$\frac{1}{2^1}= \frac{1}{2}< 2$$ which is certainly true.

Now, assume that, for some positive integer, k, $$\frac{k}{2^k}< 2$$. We want to use that to prove that $$\frac{k+1}{2^{k+1}}< 2$$. First an obvious step- from $$\frac{k}{2^k}< 2$$, $$\frac{k+1}{2^k}= \frac{k}{2^k}+ \frac{1}{2^k}< 3$$ since $$\frac{1}{2^k}< 1$$. Now, divide both sides of $$\frac{k+1}{2^k}= \frac{k}{2^k}+ \frac{1}{2^k}< 3$$ by 2 to get $$\frac{k+1}{2^{k+1}}< \frac{3}{2}< 2$$.
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