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An exercise
Posted: Tue Nov 01, 2016 7:06 pm
by Mehedi Hasan Nowshad
Let $a_1,a_2,......a_n$ are positive real numbers such that $\sum_{i=1}^{n} \dfrac{1}{a_i} = 1$. Prove that,
\[ \sum_{i=1}^{n} \dfrac{a_i^2}{i} > \dfrac{2n}{n+1} \]
Re: An exercise
Posted: Thu Nov 03, 2016 1:00 pm
by SYED ASHFAQ TASIN
I have a problem in this,have to see the ans!(╯﹏╰）
Re: An exercise
Posted: Fri Nov 04, 2016 12:23 am
by asif e elahi
Mehedi Hasan Nowshad wrote:Let $a_1,a_2,......a_n$ are positive real numbers such that $\sum_{i=1}^{n} \dfrac{1}{a_i} = 1$. Prove that,
\[ \sum_{i=1}^{n} \dfrac{a_i^2}{i} > \dfrac{2n}{n+1} \]
Wrong for $n=1$.
Hint
Re: An exercise
Posted: Fri Nov 04, 2016 8:23 pm
by Mehedi Hasan Nowshad
oops! I forgot about the case for n=1. :3