Cálculo III: Soma da série -Lista de Exercício
Em cada série abaixo, determinar o valor da soma da série no caso de ela convergir.
| (a)$ \displaystyle\sum_{n=0}^{\infty} \left( \frac{2}{3}\right)^{n} $ |
(b)$\displaystyle\sum_{n=3}^{\infty}4\left( \frac{2}{3}\right)^{n} $ |
(c)$\displaystyle\sum_{n=1}^{\infty} \frac{ 3}{9n^2+3n_2} $ |
$\quad $ (d)$ \displaystyle\sum_{n=1}^{\infty} \ln{\left( \frac{n}{n+1}\right)} $ |
(e)$ \displaystyle\sum_{n=1}^{\infty} 2^{2-n} $ |
| (f)$ \displaystyle\sum_{n=1}^{\infty} \frac{2n+1}{n^2(n+1)^{2}} $ |
(g) $ \displaystyle\sum_{n=1}^{\infty}\left[ \frac{1}{2^{n-2}} - \frac{1}{3^{n+2}}\right] $ |
(h) $ \displaystyle\sum_{n=1}^{\infty} \left[ \frac{1}{2^{n}} - \frac{1}{3^{n}} \right] $ |
(i)$ \displaystyle\sum_{n=1}^{\infty} \frac{1}{4n^{n} - 1} $ |
$\quad $ (j) $ \displaystyle\sum_{n=1}^{\infty} \frac{ (-2)^{n+2} }{ 3^{n+1}} $ |
| (k)$ \displaystyle\sum_{n=1}^{\infty} \frac{2}{ (4n-3)(4n+1)} $ |
$\quad $ (l)$ \displaystyle\sum_{n=1}^{\infty}\ln{\left[ \frac{ (n+1)^{2} }{n(n+2)} \right]} $ |
(m)$ \displaystyle\sum_{n=1}^{\infty} \frac{ 2^{n+1}}{3^{2n}} $ |
(n)$\displaystyle\sum_{n=1}^{\infty} \left[ \frac{ 2^{n}\mathrm{sen}(n\pi + \pi /2 )}{3^{2n-2}} \right] $ |
(o)$ \displaystyle\sum_{n=1}^{\infty} \frac{(-1)^{n+2} 2^{n+2}}{3^{n}} $ |
Respostas
| $\qquad \quad $ (a)$ 3$ |
$\quad $(b)$\frac{32}{75} $ |
$\quad $(c)$\frac{1}{2} $ |
$\quad $(d)$-\infty $ |
$\quad $(e)$4 $ |
$\quad $(f)$1 $ |
$\quad $(g)$ \frac{71}{18} $ |
$\quad $(h)$ \frac{3}{2}$ |
$\quad $(i)$ \frac{1}{2} $ |
$\quad $(j)$-\frac{8}{5} $ |
| $\qquad \quad $(k)$ -\frac{1}{2} $ |
$\quad $(l)$ \ln{(2)} $ |
$\quad $(m)$ \frac{4}{7} $ |
$\quad $(n)$ -\frac{18}{11} $ |
$\quad $(o)$ -\frac{8}{5} $ |
Créditos da seleção e organização dos exercícios
Profº. Msc. Gilberto da Silva Pina CETEC-UFRB. Currículo Lattes. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
