1
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1answer
42 views

How to prove that $n^{\log_{2} (n) } = O (2^n) $ ?

While trying to prove that $$ n^{\log_{2} (n) } = O (2^n) , $$ I figured that $$ 2^n = e^{ n \ln (2) } , $$ and that $$ n^{ \log_{2} (n) } = n^{ \frac{\ln(n) }{ \ln(2) } } = e^{ \ln (n^{ \frac{ ...
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2answers
51 views

Not able to solve the below mentioned inequality. Someone please explain me it's solution.

This is an in equality with a solution given below. I'm not able to understand it. It will be very helpful if someone can help me understand it. Thanks. The inequality is in the image attached with ...
1
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0answers
85 views

Solving a non-linear inequality related to geometric Brownian motion

Consider the non linear inequality $$\sum_{i=1}^{n}a_{i}u^{\sum\limits_{j=1}^{i}y_j} > c$$ $$y_j \in \{0,1\}, j=1,2,\dots,n$$ $$a_i \in \mathbb{R}, i=1,2,\dots,n$$ $$n \in \mathbb{N}, u>0, c ...