Tagged Questions
1
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2answers
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Induction proof [ little-o notation ]
I have to prove that $ 2^n = o(n!) $, that is, $ \forall c \gt 0 \quad \exists$ $ n_0 \in \mathbb N$ such that $ \forall n \ge n_0$ we have $ 2^n \lt c.n! $
Well, this is what I did so far:
First I ...
2
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2answers
148 views
Induction Proof: $\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2 $
Prove by Mathematical Induction . . .
$$\sum_{i=1}^{n+1} i \cdot 2^i = n \cdot 2^{n+2}+2 $$
for all $n \geq 0$
I tried solving it, but I got stuck near the end . . .
a. Basis Step:
$1\cdot 2^1 ...
1
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0answers
44 views
Want to show the a proof of the sequent $\forall x \forall y R(x,y) \Rightarrow R(y,y)$ must have a cut
Want to show the a proof of the sequent $\forall x \forall y R(x,y) \Rightarrow R(y,y)$ must have a cut. For this question we are in the Gentzen calculus. I am even having trouble just finding a ...
1
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2answers
79 views
Modulo Theorem proof
How do i prove the following theorem?
Supose $p$ is a prime number, $r,\ s$ are positive integers and $x$ is an arbitary integer. Then we have $x^r \equiv x^s\ (mod\ p)$ whenever $r \equiv s \ (mod \ ...
