BC Calculus Series Test

The coefficient of the

 $\sum_{n=1}^{\infty}\left(\frac{1}{3}\right)^{2n}$  =

The coefficient of  $\left(x-1\right)^5$  in the Taylor Series for  $f\left(x\right)=\ln x$  about x = 1 is

The series $\sum_{n=0}^{\infty}\left(-9\right)^n\ \frac{x^{4n}}{\left(2n\right)!}$  represents which function below?

Which of the following series converge?

Consider the series $\sum_{n=1}^{\infty}\frac{2^n}{\left(n+1\right)!}$   If the Ratio Test is applied to this series, which of the following inequalities indicates that the series is convergent?

What is the sum of the series

Which of the following series diverge?   $I.\ \ \ \ \sum_{n=0}^{\infty}\left(\frac{e}{\pi}\right)^n$   $II.\ \ \ \ \sum_{n=1}^{\infty}\frac{\sqrt{n}}{n^2}\ \ \$   $III.\ \ \ \ \sum_{n=1}^{\infty}\frac{n!}{3^n}\$  

Let  $P\left(x\right)=3x^2-5x^3+7x^4+3x^5$  be the fifth-degree Taylor Polynomial for the function f about x = 0.  What is the value of  $f'''\left(0\right)$  ?

Which of the following is the series for  $f\left(x\right)=x\left(\cos x-1\right)$