Infinite series

2010006905

Level:

Evaluate the following infinite sum.

\sum_{n = 1}^{\infty} {(- \frac{3}{5})}^{n}

- \frac{3}{8}

- \frac{3}{2}

\frac{3}{2}

\frac{3}{8}

2010006904

Level:

We are given the equation

\sum_{n = 0}^{\infty} \frac{(x + 2)^{n}}{3^{n}} = \frac{x + 3}{2 x + 1}

with the unknown

x

being a real number. What is the set of all its solutions?

{0}

{- 8; 0}

{}

{- 6; 2}

{- 8}

2010006903

Level:

What is the sum of the repeating numbers

0. \overset{―}{45}

and

0.2 \overset{―}{81}

\frac{81}{110}

\frac{59}{110}

\frac{110}{81}

\frac{36}{110}

\frac{81}{100}

2010006902

Level:

The sum of the infinite geometric series

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

is equal to:

1 + \sqrt{3}

\sqrt{3} - 1

\frac{3 - \sqrt{3}}{3}

\frac{\sqrt{3} - 3}{3}

\sqrt{3}

2010006901

Level:

We are given an infinite geometric series:

(\sqrt{2} - \sqrt{7}) + (2 - \sqrt{14}) + (2 \sqrt{2} - 2 \sqrt{7}) + \dots .

What is the value of its common ratio?

\sqrt{2}

\sqrt{2} - \sqrt{7}

2

7

\sqrt{2} - 2

Common Ratio of Infinite Geometric Series

Submitted by ladislav.foltyn on Fri, 05/03/2019 - 10:43

Question:

In each line of the table, mark the interval to which the common ratio of the given infinite geometric series belongs.

Sum of Infinite Geometric Series I

Submitted by ladislav.foltyn on Sat, 02/23/2019 - 13:30

1003108809

Level:

We are given the equation

\sum_{n = 1}^{\infty} (\sin x)^{2 n - 2} = 2 \cdot tg x

with the unknown

x

being a real number. What is the set of all its solutions?

⋃_{k \in Z} {\frac{1}{4} π + k \cdot π}

⋃_{k \in Z} {\frac{3}{4} π + k \cdot π}

⋃_{k \in Z} {\frac{3}{4} π + k \cdot \frac{π}{2}}

⋃_{k \in Z} {\frac{1}{8} π + k \cdot \frac{π}{2}}

⋃_{k \in Z} {\frac{1}{4} π + k \cdot \frac{π}{2}}

1003108808

Level:

We are given the equation

\sum_{n = 1}^{\infty} 2^{n x} = 1

with the unknown

x

being a real number. What is the set of all its solutions?

{- 1}

{1}

{1; - 1}

{}

{0}

1003108807

Level:

We are given the equation

\log x + \log \sqrt{x} + \log \sqrt[4]{x} + \log \sqrt[8]{x} + \dots = 2

with the unknown

x

being a real number. What is the set of all its solutions?

{10}

{1}

{100}

{}

{\frac{1}{10}}

2010006905

2010006904

2010006903

2010006902

2010006901

Common Ratio of Infinite Geometric Series

Sum of Infinite Geometric Series I

1003108809

1003108808

1003108807

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