Examples of MathJax copied from Dr. Theral Moore’s site.
- Use integration to find the Maclaurin series for \(\ln(1+x)\).
- Give the sum of the series \(\quad\quad \displaystyle 1+\ln 3+\frac{(\ln 3)^2}{2!}+\frac{(\ln 3)^3}{3!}+\cdots.\)
In 3–6, test each series for convergence or divergence. Use the indicated test.
- \(\quad\quad\displaystyle \sum_{n=1}^{\infty}\ \frac{n^2+n+2}{(n^2+4) 3^{n}}\quad \)LCT
- \(\quad\quad\displaystyle \sum_{n=2}^{\infty}\ \frac{1}{(\ln n)^{\ln^n}}\quad \)CT
- \(\quad\quad\displaystyle \sum_{n=1}^{\infty}\ \frac{\sin \frac{1}{n}}{n} \quad\) LCT
- \(\quad\quad \displaystyle\sum_{n=1}^{\infty}\ \frac{3^n}{n^n}\quad\)Root Test
- Find the interval of convergence for \(\displaystyle \sum_{n=2}^{\infty}\ \frac{(x-4)^n}{2^n \ln n}\)