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4
questions with no upvoted or accepted answers
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How to prove the following inequality with complete induction?
Let $n \in \mathbb{N}$, and let $a_1, ... , a_n > 0.$
Show that:
I got the hint that we have to use this induction step for the induction proof:
And thats what I got so far in the Induction step ...
- 33
1
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Where has this inequality come from?
Within the paper PRIMES is in P the following inequality can be found (on page 4, in the proof of Lemma 4.3)
$$
n^{\lfloor \log(B) \rfloor} \prod_{i=1}^{\lfloor \log^2(n) \rfloor} (n^i - 1) \hspace{...
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Induction proof for product of $a^x$ is less than or equal to the sum of $x\times a$
So this type of problem has me stuck in proving some relation. I assumed to use induction but I am stuck at a certain step and cannot understand if there is a trick or perhaps my idea is just wrong:
...
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Inequality with Products and Sums
I need help to find a proof for the following inquality.
Assuming that $ 0 \leq c_i \leq 1 $ and $ 0 \leq d_i \leq 1 $, show that
$$
\prod_{i=1}^N (c_i + d_i - c_i d_i) \geq \prod_{i=1}^N c_i + \prod_{...
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