Calculus Test (a test for JAWS)

• Use integration to find the Maclaurin series for \(\ln(1+x)\).
• Give the sum of the series \(1+\ln 3+\frac{(\ln 3)^2}{2!}+\frac{(\ln 3)^3}{3!}+\cdots.\)

In 1-4, test each series for convergence or divergence. Use the indicated test.

1. \(\sum_{n=1}^{\infty}\ \frac{n^2+n+2}{(n^2+4) 3^{n}}\)      LCT
2. \(\sum_{n=2}^{\infty}\frac{1}{(\ln n)^{\ln n}}\)      CT
3. \(\sum_{n=1}^{\infty}\ \frac{\sin \frac{1}{n}}{n} \)   LCT
4. Use the Root Test. $$\sum_{n=1}^{\infty}\ \frac{3^n}{n^n}$$
5.  $$\sum_{n=1}^{\infty}\frac{1}{n^3 }=\int_1 ^{\infty}\frac{dx}{x^3 + 1}$$

This is a test to see how well the screen reader JAWS will read the math symbols without the Latex extra space command of ‘\quad.’ Also Note that the last line is thrown into display mode and so sum (summation) symbol is centered on the page and appears like this:
$$\sum_{n=1}^{\infty}$$