Science:Infinite Series Module/Quizzes/Quiz Questions

Quiz 1

$a_{k} = \sin (\frac{2 π k}{4 + 4 k})$

$\frac{1}{\sqrt{2}}$

$\sum_{k = 2}^{\infty} \frac{4^{k - 2}}{5^{k - 1}}$

$\sum_{k = 1}^{\infty} (\frac{1}{k + 4} - \frac{1}{k + 5})$

$a_{n} = {\begin{cases} 2 - \frac{1}{n} & if n is odd \\ 1 + \frac{1}{n} & if n is even \end{cases}$

$\frac{1}{1} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \dots$

$\sum_{k = 1}^{\infty} \frac{(x - 1)^{k} (k + 2)}{2^{k} (k + 3)}$

$\sum_{k = 1}^{\infty} \ln (\frac{k^{2} + 3}{k^{2} + 2 k + 4})$

$\sum_{k = 1}^{\infty} \frac{k^{k}}{(3 k)!}$

$\sum_{k = 1}^{\infty} \frac{(- 1)^{k}}{k - p}$

$f (x) = \frac{4}{16 x^{2} - 1}$

$f (x) = e^{5 x} \cos (5 x)$

Equation 1

$\int e^{- x^{2}} d x$

Equation 2

$D + x + \frac{x^{3}}{a} + \dots$

$f (x) = \frac{\sin (2 x)}{3 x}$

$\sum_{k = 0}^{\infty} \frac{x^{8 k}}{k!}$