9000063602
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }(-1)^{n} \frac{3}
{2n + 1}
\]
\(0\)
\(-\frac{3}
{2}\)
\(\frac{3}
{2}\)
\(- 1\)
Limit of a sequence
9000063603
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\frac{2n^{2} + 1}
{3n - 1}
\]
\(\infty \)
\(\frac{3}
{2}\)
\(0\)
\(- 1\)
9000063604
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\sin 2\pi n
\]
\(0\)
\(1\)
\(- 1\)
\(\infty \)
9000063605
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\log 3^{n}
\]
\(\infty \)
\(- 1\)
\(0\)
\(3\)
9000063606
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\frac{3n^{2} - 2n + 1}
{2n^{3} - 4}
\]
\(0\)
\(\frac{3}
{2}\)
\(\frac{1}
{2}\)
\(-\frac{1}
{4}\)
9000063607
Level:
B
Find the following limit.
\[
\lim _{n\to \infty } \frac{1}
{\log 10^{n}}
\]
\(0\)
\(1\)
\(10\)
\(\infty \)
9000063608
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\frac{2^{n} + 3^{n}}
{3^{n}}
\]
\(1\)
\(2\)
\(3\)
\(\infty \)
9000063609
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\left ( \frac{n}
{n - 1} + \frac{n + 2}
{n + 1}\right )
\]
\(2\)
\(- 1\)
\(0\)
\(1\)
9000064008
Level:
C
Find the limit of the following sequence.
\[
{\left(\frac{(n^{2} + 2n + 1)^{n}}
{n^{2n}} \right)}_{n=1}^{\infty }
\]
Hint: The limit of the sequence \({\bigl ({\bigl (1 + \frac{1}
{n}\bigr )}^{n}\bigr )}_{n=1}^{\infty }\)
is the Euler number \(\mathrm{e}\).
\(\mathrm{e}^{2}\)
\(2\mathrm{e}\)
\(\mathrm{e} + 2\)
\(\infty \)
9000064009
Level:
C
Find the limit of the following sequence.
\[
{\left({\Bigl (\frac{\root{n}\of{2}}
{n} + \root{n}\of{2}\Bigr )}^{n}\right)}_{
n=1}^{\infty }
\]
Hint: The limit of the sequence \({\bigl ({\bigl (1 + \frac{1}
{n}\bigr )}^{n}\bigr )}_{n=1}^{\infty }\)
is the Euler number \(\mathrm{e}\).
\(2\mathrm{e}\)
\(\mathrm{e}^{2}\)
\(\mathrm{e} + 2\)
\(\infty \)