1003047503
Level:
B
Choose the sequence with the limit equal to \( -5 \).
\( (0.15^n-5)_{n=1}^{\infty} \)
\( ((-5)^n-0.15)_{n=1}^{\infty} \)
\( (5^n-5)_{n=1}^{\infty} \)
\( (5^n+5)_{n=1}^{\infty} \)
\( (-0.15^n+5)_{n=1}^{\infty} \)
Limit of a sequence
1003047502
Level:
C
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}\frac 4{2\sqrt{n}-3} \]
\( 0 \)
\( 2 \)
\( \frac12 \)
\( 4 \)
\( \infty \)
1003047501
Level:
C
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}(2\sqrt{n}-3) \]
\( \infty \)
\( 2 \)
\( -1 \)
\( 0 \)
\( -3 \)
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 \(\mathrm{e}\).
\(2\mathrm{e}\)
\(\mathrm{e}^{2}\)
\(\mathrm{e} + 2\)
\(\infty \)
9000064010
Level:
C
Find the limit of the following sequence.
\[
{\left({\Bigl (\frac{2n + 1}
{n} \Bigr )}^{n}\right)}_{
n=1}^{\infty }
\]
Hint: The limit of the sequence \({\bigl ({\bigl (1 + \frac{1}
{n}\bigr )}^{n}\bigr )}_{n=1}^{\infty }\)
is the Euler number \(\mathrm{e}\).
\(\infty \)
\(2\mathrm{e}\)
\(\mathrm{e}^{2}\)
\(\mathrm{e} + 2\)
9000063610
Level:
C
Find the following limit.
\[
\lim _{n\to \infty } \frac{3 + 6 + 9 +\cdots +3n}
{6 + 12 + 18 +\cdots +6n}
\]
\(\frac{1}
{2}\)
\(0\)
\(1\)
\(\infty \)
9000064002
Level:
C
Consider the convergent sequence
\[
\left ( \frac{5 - n}
{2n - 1}\right )_{n=1}^{\infty }
\]
and its limit \(L\).
Find the index of the first term of the sequence which differs from
\(L\) by less
than \(\frac{1}
{100}\).
\(226\)
\(450\)
\(452\)
\(451\)
\(225\)
9000064001
Level:
C
Consider the sequence
\[
\left (\frac{(-1)^{n}}
{n} + 3\right )_{n=1}^{\infty }
\]
and its limit \(L\). How many terms
of the sequence differ from \(L\)
by more than \(\frac{1}
{50}\)?
\(49\)
\(50\)
\(10\)
\(100\)