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. \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\frac{{{1}}}{{{n}+{3}}}}\)

Find the power series representation for g centered at 0 by differentiating or integrating the power series for f(perhaps more than once). Give the interval of convergence for the resulting series. \(g(x)=\ln(1-2x)\) using \(f(x)=\frac11-2x\)

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. \(\frac13+\frac15+\frac17+\frac19+\frac{1}{11}+...\)

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. \(\displaystyle{\sum_{{{n}={2}}}^{\infty}}{\frac{{{1}}}{{{n}\sqrt{{{\ln{{n}}}}}}}}\)