1003108711
Level:
A
The sum of the infinite geometric series
\[ 1-\frac34+\frac9{16}-\frac{27}{64}+\dots \]
is equal to:
\( \frac47 \)
\( \frac14 \)
\( 4 \)
\( \frac74 \)
\( \frac57 \)
Infinite series
1003108712
Level:
A
The value of the expression
\[ \sum\limits_{n=1}^{\infty}(-1)^n\cdot\left(\frac23\right)^n \]
is equal to:
\( -\frac25 \)
\( \frac25 \)
\( -\frac23 \)
\( \frac23 \)
\( \frac52 \)
1003108713
Level:
A
The value of the expression
\[ \sum\limits_{n=1}^{\infty}\left(\frac13\right)^n \]
is equal to:
\( \frac12 \)
\( 2 \)
\( 1 \)
\( \frac14 \)
\( \frac23 \)
2010006901
Level:
A
We are given an infinite geometric series:
\[ \left(\sqrt2-\sqrt7\right)+\left(2-\sqrt{14}\right)+\left(2\sqrt2-2\sqrt{7}\right)+\dots\text{ .} \]
What is the value of its common ratio?
\( \sqrt{2} \)
\( \sqrt{2} - \sqrt{7}\)
\(2\)
\(7\)
\( \sqrt{2} - 2\)
2010006902
Level:
A
The sum of the infinite geometric series
\[ \left(\sqrt3-1\right)+\left(\sqrt3-1\right)^2+\left(\sqrt3-1\right)^3+\dots \]
is equal to:
\( 1+\sqrt3 \)
\(\sqrt3-1 \)
\( \frac{3-\sqrt{3}}{3}\)
\( \frac{\sqrt{3}-3}{3}\)
\( \sqrt3\)
2010006905
Level:
A
Evaluate the following infinite sum.
\[
\sum _{n=1}^{\infty }\left (-\frac{3}
{5}\right )^{n}
\]
\(- \frac{3}
{8}\)
\(- \frac{3}
{2}\)
\(\frac{3}
{2}\)
\(\frac{3}
{8}\)
2010006908
Level:
A
Find the sum of the following infinite series.
\[
\sum _{n=1}^{\infty }\left (\frac{\sqrt{5} - 1}
{\sqrt{5}} \right )^{n-1}
\]
\( \sqrt{5} \)
\( \frac{\sqrt{5}}{5}\)
\( \frac{\sqrt{5}-1}{5}\)
Series diverges.
2010006909
Level:
A
Evaluate the following infinite sum.
\[
-\frac{3}
{4} + \frac{1}
{4} -\frac{3}
{8} + \frac{1}
{8} - \frac{3}
{16} +\cdots
\]
\( -1 \)
\(-\frac{1}
{4}\)
\(-\frac{1}
{2}\)
\( -2 \)
2010006911
Level:
A
Find the sum of the following geometric series.
\[
-\frac{1}
{2} + \frac{1}
{6} - \frac{1}
{18} + \frac{1}
{48}-\cdots
\]
\(-\frac{3}
{8}\)
\(-\frac{3}
{4}\)
\(\frac{3}
{8}\)
\( \infty \)
9000062901
Level:
A
Find the sum of the following geometric series.
\[
-\frac{1}
{3} + \frac{1}
{6} - \frac{1}
{12} + \frac{1}
{24}-\cdots
\]
\(-\frac{2}
{9}\)
\(-\frac{2}
{3}\)
\(\frac{2}
{9}\)
\(\infty \)