Test the series for convergence or divergence. \

$$\sum_{n=1}^{\infty}\left(\dfrac{3 n}{1+8 n}\right)^n$$

Use the binomial series to expand the function as a power series. State the radius of convergence. \

$$\dfrac{1}{\sqrt[3]{32-x}}$$

Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why. $\sum_{n=1}^{\infty}(0.6)^{n-1}$

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

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

Use series to evaluate the following limit.

$$lim x→0 sin x-x/x^3$$

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

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

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