\( \newcommand{\combin}[2]{{}^{#1}C_{#2} } \newcommand{\cmod}[3]{#1 \equiv #2\left(\bmod {}{#3}\right)} \newcommand{\mdc}[2]{\left( {#1},{#2}\right)} \newcommand{\mmc}[2]{\left[ {#1},{#2}\right]} \newcommand{\cis}{\mathop{\rm cis}} \newcommand{\sen}{\mathop{\rm sen}} \newcommand{\senq}{\mathop{\rm sen^2}} \newcommand{\tg}{\mathop{\rm tg}} \newcommand{\tgq}{\mathop{\rm tg^2}} \newcommand{\arctg}{\mathop{\rm arctg}} \newcommand{\arcsen}{\mathop{\rm arcsen}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\tr}[1]{ \textnormal{Tr}\left({#1}\right)} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\H}{\mathbb{H}} \newcommand{\vect}[1]{\overrightarrow{#1}} \newcommand{\Mod}[1]{\ (\mathrm{mod}\ #1)} \)

quarta-feira, 17 de janeiro de 2018

Exercícios com séries de Mengoli

Exercício:(Nível de dificuldade: muito baixo)
Determine o valor das somas das seguintes séries
a) \[ \sum\limits_{n \ge 4}^{} {\frac{{12}}{{(3n - 1)(3n + 5)}}} \]

\[\frac{25}{77}\]

b) \[ \sum\limits_{n \ge 2}^{} {\frac{{36}}{{(4n - 3)(4n + 9)}}} \]

\[\frac{227}{195}\]

c) \[ \sum\limits_{n \ge 3}^{} {\frac{{180}}{{(9n - 4)(9n + 32)}}} \]

\[\frac{89863}{150880}\]

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