limita

dtiwari · Mesaj de **dtiwari** » 24 Dec 2018, 07:39

For a given sequence $a_{1},a_{2},a_{3},....,a_{n}$ .

If $\displaystyle \lim_{n\rightarrow \infty} a_{n} = a.$ Then $\displaystyle \lim_{n\rightarrow \infty}\frac{1}{\ln (n)}\sum^{n}_{k=1}\frac{a_{k}}{k}$

Mesaj de **ghioknt** » 24 Dec 2018, 22:02

Stolz-Cesaro: $x_n=\sum_{k=1}^{n}\frac{a_k}{k},\;y_n=\ln n$
$\frac{x_{n+1}-x_n}{y_{n+1}-y_n}=\frac{\frac{a_{n+1}}{n+1}}{\ln (n+1)-\ln n}=\frac{a_{n+1}\cdot \frac{n}{n+1}}{\ln (1+\frac{1}{n})^n}$ etc.

dtiwari · Mesaj de **dtiwari** » 21 Mai 2019, 11:33

Thanks Professor.

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