9000063807
Level:
A
Among the numbers \(5\),
\(15\),
\(28\),
\(47\)
identify the number which is not a member of the sequence
\(\left (2n^{2} - 3\right )_{n=1}^{\infty }\).
\(28\)
\(5\)
\(15\)
\(47\)
A
9000063810
Level:
A
Consider the sequences \(\left (a_{n}\right )_{n=1}^{\infty }\)
and \(\left (b_{n}\right )_{n=1}^{\infty }\)
where \(a_{n} = 2^{n}\)
and \(b_{n} = n^{2} - 1\),
respectively. Identify a true statement in the terms of these sequences.
\(a_{3} = b_{3}\)
\(a_{2} = b_{2} + 2\)
\(a_{4} = b_{4} - 2\)
\(a_{5} = b_{5} - 8\)
9000063401
Level:
A
Identify the quotient of the geometric series
\(\sum _{n=1}^{\infty } \frac{1}
{2^{n-3}} \).
\(\frac{1}
{2}\)
\(2\)
\(1\)
\(\frac{1}
{8}\)
9000063402
Level:
A
Identify the quotient of the geometric series
\(\sum _{n=1}^{\infty }3^{2-n}\).
\(\frac{1}
{3}\)
\(1\)
\(\frac{1}
{9}\)
\(-\frac{1}
{9}\)
9000063406
Level:
A
Evaluate the following infinite sum.
\[
\sum _{n=1}^{\infty }\left (-\frac{1}
{2}\right )^{n+2}
\]
\(- \frac{1}
{12}\)
\(-\frac{1}
{8}\)
\(\frac{1}
{2}\)
\(1\)
9000063405
Level:
A
Evaluate the following infinite sum.
\[
-\frac{2}
{3} + \frac{1}
{6} -\frac{2}
{6} + \frac{1}
{12} - \frac{2}
{12} + \frac{1}
{24}+\cdots
\]
\(- 1\)
\(-\frac{4}
{3}\)
\(\frac{1}
{3}\)
\(\frac{3}
{2}\)
9000063601
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\frac{2n + 3}
{3n - 2}
\]
\(\frac{2}
{3}\)
\(-\frac{3}
{2}\)
\(0\)
\(1\)
9000062902
Level:
A
Find the sum of the following geometric series.
\[
1 + \frac{3}
{2} + \frac{9}
{4} + \frac{27}
{8} + \frac{81}
{16}+\cdots
\]
\(\infty \)
\(- 2\)
\(2\)
\(\frac{2}
{5}\)
9000062405
Level:
A
Evaluate the following one-sided limit.
\[
\lim _{x\to 6^{-}}\frac{3x + 2}
{x - 6}
\]
\(-\infty \)
\(1\)
\(+\infty \)
\(0\)
9000062901
Level:
A
Find the sum of the following geometric series.
\[
-\frac{1}
{3} + \frac{1}
{6} - \frac{1}
{12} + \frac{1}
{24}-\cdots
\]
\(-\frac{2}
{9}\)
\(-\frac{2}
{3}\)
\(\frac{2}
{9}\)
\(\infty \)