Does the series $9+10+\frac{100}{9}+\frac{1000}{81}+\cdots$ converge?

What is the common ratio of the series $9-\frac{27}{10}+\frac{81}{100}-\frac{243}{1000}+\cdots$?

Find the sum of the infinite series $8-3+\frac{9}{8}-\frac{27}{64}+\cdots$.

Does the series $9-\frac{3}{2}+\frac{1}{4}-\frac{1}{24}+\cdots$ converge?

Evaluate ${\sum }_{n=1}^{\infty }12{\left(-\frac{1}{3}\right)}^{n-1}$, giving an exact fraction.

An infinite geometric series has first term $6$ and sum $30$. What is its common ratio?

Evaluate ${\sum }_{n=1}^{\infty }9{\left(-\frac{6}{7}\right)}^{n-1}$, giving an exact fraction.

What is the common ratio of the series $18-\frac{63}{2}+\frac{441}{8}-\frac{3087}{32}+\cdots$?

Does the series $6+54+486+4374+\cdots$ converge?

Evaluate ${\sum }_{n=1}^{\infty }8{\left(\frac{4}{7}\right)}^{n-1}$, giving an exact fraction.

Find the sum of the infinite series $36+\frac{108}{7}+\frac{324}{49}+\frac{972}{343}+\cdots$.

Evaluate ${\sum }_{n=1}^{\infty }10{\left(\frac{3}{4}\right)}^{n-1}$, giving an exact fraction.

An infinite geometric series has first term $8$ and sum $48$. What is its common ratio?

Find the sum of the infinite series $4+\frac{4}{5}+\frac{4}{25}+\frac{4}{125}+\cdots$.

Does the series $5+\frac{20}{3}+\frac{80}{9}+\frac{320}{27}+\cdots$ converge?

What is the common ratio of the series $12-4+\frac{4}{3}-\frac{4}{9}+\cdots$?

Find the sum of the infinite series $21+\frac{63}{10}+\frac{189}{100}+\frac{567}{1000}+\cdots$.

Find the sum of the infinite series $18-\frac{81}{5}+\frac{729}{50}-\frac{6561}{500}+\cdots$.

Find the sum of the infinite series $10-\frac{10}{9}+\frac{10}{81}-\frac{10}{729}+\cdots$.

An infinite geometric series has first term $6$ and sum $16$. What is its common ratio?

An infinite geometric series has first term $12$ and sum $54$. What is its common ratio?

Evaluate ${\sum }_{n=1}^{\infty }3{\left(\frac{3}{5}\right)}^{n-1}$, giving an exact fraction.

Find the sum of the infinite series $9+\frac{18}{5}+\frac{36}{25}+\frac{72}{125}+\cdots$.

Find the sum of the infinite series $30+\frac{70}{3}+\frac{490}{27}+\frac{3430}{243}+\cdots$.

Evaluate ${\sum }_{n=1}^{\infty }15{\left(\frac{7}{9}\right)}^{n-1}$, giving an exact fraction.

Does the series $12-\frac{72}{7}+\frac{432}{49}-\frac{2592}{343}+\cdots$ converge?

The repeating decimal $0.\overline{6}$ is the sum of an infinite geometric series whose first term is $\frac{6}{10}$. What fraction does it equal, in lowest terms?

Find the sum of the infinite series $27-\frac{189}{8}+\frac{1323}{64}-\frac{9261}{512}+\cdots$.

The repeating decimal $0.\overline{54}$ is the sum of an infinite geometric series whose first term is $\frac{54}{100}$. What fraction does it equal, in lowest terms?

The repeating decimal $0.\overline{36}$ is the sum of an infinite geometric series whose first term is $\frac{36}{100}$. What fraction does it equal, in lowest terms?

What is the common ratio of the series $18-\frac{90}{7}+\frac{450}{49}-\frac{2250}{343}+\cdots$?

What is the common ratio of the series $18+\frac{81}{2}+\frac{729}{8}+\frac{6561}{32}+\cdots$?

Find the sum of the infinite series $8+1+\frac{1}{8}+\frac{1}{64}+\cdots$.

The repeating decimal $0.\overline{63}$ is the sum of an infinite geometric series whose first term is $\frac{63}{100}$. What fraction does it equal, in lowest terms?

The repeating decimal $0.\overline{246}$ is the sum of an infinite geometric series whose first term is $\frac{246}{1000}$. What fraction does it equal, in lowest terms?

An infinite geometric series has first term $18$ and sum $81$. What is its common ratio?

What is the common ratio of the series $6-\frac{14}{3}+\frac{98}{27}-\frac{686}{243}+\cdots$?

Does the series $9+\frac{54}{5}+\frac{324}{25}+\frac{1944}{125}+\cdots$ converge?

Does the series $20-\frac{10}{3}+\frac{5}{9}-\frac{5}{54}+\cdots$ converge?

Does the series $12+\frac{120}{7}+\frac{1200}{49}+\frac{12000}{343}+\cdots$ converge?