Classify whether this series convergessum_(k = 1)^oo ((-1)^k xx k)

How do you find the Maclaurin series of ${\displaystyle f\left(x\right)=\ln (1+x)?}$

Tell whether the series converge. If it converges, find the sum.
1) ${\displaystyle \sum _{n=0}^{\mathrm{\infty }}{\left(\frac{\pi }{2}\right)}^n}$
2) ${\displaystyle \sum _{n=1}^{\mathrm{\infty }}{\left(\frac{3}{7}\right)}^n}$

Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.
${\displaystyle \sum _{n=2}^{\mathrm{\infty }}\frac{1}{n\sqrt{\ln n}}}$

The next number in the series 3, 4, 6, 7, 9, 10 is: 12 11 15 17 13

Find the sim of each of the following series.
1) $\sum _{n=1}^{\mathrm{\infty }}n{x}^n,|x|<1$
2) $\sum _{n=1}^{\mathrm{\infty }}\frac{n}{8^n}$

In series A, the first term is 2, and the common ratio is 0.5. In series B, the first term is 3, and the two infinite series have the same sum. What is the ratio in series B?​

Write out he first four terms of the Maclaurin series of f(x) if ${\displaystyle f\left(0\right)=2,f^{\prime }\left(0\right)=3,f{}^{″}\left(0\right)=4,f{}^{‴}\left(0\right)=12}$