Sequence and series (1 Viewer)

juantheron · Nov 28, 2017

$Let $\displaystyle a_{n} = n+\frac{1}{n}$ for $n=1,2,3,4,....20$ and $p=\frac{1}{20}\sum^{20}_{n=1}a_{n}$

$And $q = \frac{1}{20}\sum^{20}_{n=1}\frac{1}{a_{n}}$. Then proving $q\in \left(0,\frac{21-p}{21}\right)$ .

Trial $p = \frac{1}{20}\left((1+2+3+\cdot +20)+1+\frac{1}{2}+\frac{1}{3}+\cdots +\frac{1}{20}\right))$

$\approx 11.5+\frac{2.303}{20} \log_{10}(20) \approx 11.5$

now how to solve further, help me

camelrider · Nov 29, 2017

juantheron · Nov 30, 2017

Thanks camelrider.

Sequence and series (1 Viewer)

juantheron

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camelrider

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juantheron

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