Infinite series

Sum of Infinite Geometric Series II

Submitted by vladimir.arzt on Thu, 09/12/2024 - 09:53

Submitted by vladimir.arzt on Wed, 08/28/2024 - 10:42

Submitted by vladimir.arzt on Wed, 08/28/2024 - 10:38

Submitted by vladimir.arzt on Wed, 08/28/2024 - 10:35

Level:

Find the sum of the following geometric series.

- \frac{1}{2} + \frac{1}{6} - \frac{1}{18} + \frac{1}{48} - \dots

- \frac{3}{8}

- \frac{3}{4}

\frac{3}{8}

\infty

Level:

Express the repeating decimal

0.4 \overset{―}{32}

as a fraction in lowest terms.

\frac{214}{495}

\frac{98}{225}

\frac{16}{495}

\frac{8}{225}

Level:

Evaluate the following infinite sum.

- \frac{3}{4} + \frac{1}{4} - \frac{3}{8} + \frac{1}{8} - \frac{3}{16} + \dots

- 1

- \frac{1}{4}

- \frac{1}{2}

- 2

Level:

Find the sum of the following infinite series.

\sum_{n = 1}^{\infty} {(\frac{\sqrt{5} - 1}{\sqrt{5}})}^{n - 1}

\sqrt{5}

\frac{\sqrt{5}}{5}

\frac{\sqrt{5} - 1}{5}

Series diverges.

Level:

Find all the values of

x

such that the following infinite series is convergent.

1 + 2 x - 3 + (2 x - 3)^{2} + (2 x - 3)^{3} + \dots

x \in (1; 2)

x \in (- \infty; - 1)

x \in (1; + \infty)

x \in R

Level:

Solve the following equation.

1 + 3 x + 9 x^{2} + \dots = 2

x = \frac{1}{6}

x = - \frac{1}{3}

x = \frac{1}{3}

The equation has no solution.