Decide ${\sum }_{n=2}^{\infty }\frac{n+1}{n^4-2n+1}$ and name the test.

Decide ${\sum }_{n=1}^{\infty }\frac{n!2^n}{\left(2n\right)!}$.

Decide ${\sum }_{n=1}^{\infty }\frac{2^{n-1}}{9^n}$ and name the reason.

Decide ${\sum }_{n=1}^{\infty }\frac{\left(3n\right)!}{{\left(n!\right)}^{3}20^n}$.

A student writes: "The terms of ${\sum }_{n=1}^{\infty }\frac{1}{n^2+9n}$ are positive, decreasing and tend to $0$, so by the Alternating Series Test the series converges." Is the argument SOUND?

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=2}^{\infty }\frac{1}{n\ln n}$?

Decide ${\sum }_{n=1}^{\infty }\frac{n+8}{n^3-9n+1}$ and name the test.

Decide ${\sum }_{n=1}^{\infty }\frac{5^{n-1}}{9^n}$ and name the reason.

Decide ${\sum }_{n=1}^{\infty }\frac{n+4}{n^2-5n+1}$ and name the test.

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=1}^{\infty }\frac{4n^2}{7n^2+1}$?

Decide ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n}{\sqrt[3]{n}}$ and name the test.

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=2}^{\infty }\frac{{\left(-1\right)}^n}{\ln n}$?

Decide ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n}{\sqrt{n}}$ and name the test.

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=1}^{\infty }\frac{5n-2}{3n+8}$?

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=1}^{\infty }\frac{3n+1}{n^3-4}$?

Decide ${\sum }_{n=1}^{\infty }\frac{n+6}{n^2-7n+1}$ and name the test.

What is the FASTEST correct conclusion about ${\sum }_{n=1}^{\infty }\frac{6n-7}{4n+8}$?

Decide ${\sum }_{n=1}^{\infty }\frac{6^{n-1}}{9^n}$ and name the reason.

What is the FASTEST correct conclusion about ${\sum }_{n=1}^{\infty }\frac{6n-9}{4n+10}$?

Decide ${\sum }_{n=1}^{\infty }\frac{4^{n}n!}{n^n}$.

Decide ${\sum }_{n=1}^{\infty }\frac{4^{n-1}}{5^n}$ and name the reason.

Decide ${\sum }_{n=1}^{\infty }\frac{n!3^n}{\left(2n\right)!}$.

Decide ${\sum }_{n=1}^{\infty }\frac{n!n!}{\left(2n\right)!}$.

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=1}^{\infty }\frac{5^{n-1}}{6^n}$?

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{\sqrt{n}+1}$?

Decide ${\sum }_{n=1}^{\infty }\frac{n^2+4}{n^4-5n+1}$ and name the test.

Decide ${\sum }_{n=1}^{\infty }\frac{2^{n-1}}{3^n}$ and name the reason.

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=1}^{\infty }\frac{n!}{5^n}$?

Decide ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^n}{n}$ and name the test.

A student writes: "The terms of ${\sum }_{n=1}^{\infty }\frac{1}{n^2+5n}$ are positive, decreasing and tend to $0$, so by the Alternating Series Test the series converges." Is the argument SOUND?

Decide ${\sum }_{n=1}^{\infty }\frac{2^{n}n!}{n^n}$.

Decide ${\sum }_{n=1}^{\infty }\frac{n+6}{n^4-7n+1}$ and name the test.

What is the FASTEST correct conclusion about ${\sum }_{n=1}^{\infty }\frac{3n-5}{6n+6}$?

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=2}^{\infty }\frac{\ln n}{n^2}$?

Which convergence test is the most efficient FIRST choice for ${\sum }_{n=1}^{\infty }\frac{3^n}{4^{n+1}}$?

What is the FASTEST correct conclusion about ${\sum }_{n=2}^{\infty }\frac{5n+8}{9n-9}$?

Decide ${\sum }_{n=1}^{\infty }\frac{{\left(-1\right)}^{n+1}}{\sqrt{n}}$ and name the test.

Decide ${\sum }_{n=1}^{\infty }\frac{3^{n-1}}{5^n}$ and name the reason.

What is the FASTEST correct conclusion about ${\sum }_{n=1}^{\infty }\frac{3n+2}{9n-3}$?

A student writes: "The terms of ${\sum }_{n=1}^{\infty }\frac{1}{n^2+9}$ are positive, decreasing and tend to $0$, so by the Alternating Series Test the series converges." Is the argument SOUND?