Find a power series representation for the function and determine the interval of convergence. \

$$f(x)=\dfrac{1}{1+9 x^2}$$

List the first five terms of the sequence. \

$$\{2 \cdot 4 \cdot 6 \cdots \cdots \cdot(2 n)\}$$

State the following. The Root Test

State the following. The Ratio Test

State the following. The Alternating Series Test

State the following. The Limit Comparison Test

State the following. The Comparison Test

State the following. The Integral Test

State the following. The Test for Divergence

Use series to evaluate the following limit.

$$lim x→0 sin x-x/x^3$$

Find the sum of the series. 3+9/2!+27/3!+81/4!+. . .

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

$$an = n/n^2+1$$

Determine whether the given sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
$a_n=\dfrac{\sqrt{n}}{n+2}$

Check your result in the previous part by graphing $\left|R_n(x)\right|$.
$f(x)=\sec x, \quad a=0, \quad n=2, \quad 0 \leqslant x \leqslant \pi / 6$