2010005406
Level:
B
Find the limit.
\[
\lim\limits_{n\rightarrow\infty}\frac{3^{n+1}-5^{n+1}}{3^{n-1}-5^{n-1}}
\]
\( 25 \)
\( \frac1{25} \)
\( 0 \)
\( \infty \)
\( 1 \)
Limit of a sequence
2010005404
Level:
B
Choose the sequence with the limit equal to \( -3 \).
\( \left(\left(\frac13\right)^n-3\right)_{n=1}^{\infty} \)
\( \left(3^n-3\right)_{n=1}^{\infty} \)
\( \left(3-3^n\right)_{n=1}^{\infty} \)
\( \left(3-\left(\frac13\right)^n\right)_{n=1}^{\infty} \)
\( \left((-3)^n-3\right)_{n=1}^{\infty} \)
2010005403
Level:
B
Find the following limit.
\[
\lim _{n\to \infty }\frac{4^{n}}
{3^{n}-4^n}
\]
\(-1\)
\(0\)
\(\infty \)
\(1 \)
2010005402
Level:
A
Find the limit.
\[
\lim\limits_{n\rightarrow\infty}\left( \frac7{n^2} +3+\frac{7-4n^2}{3+n^2}\right)
\]
\( -1 \)
\( 0 \)
\( \infty \)
\( -\infty \)
\(1 \)
2010005401
Level:
A
Find the following limit.
\[
\lim _{n\to \infty }\left ( \frac{n+1}
{n - 1} + \frac{n -1}
{n + 1}\right )
\]
\(2\)
\(-1\)
\(0\)
\(1\)
2010005309
Level:
C
Find the limit
\[
\lim\limits_{n\to\infty} \left( \frac{1+2+3+\dots+n}{1-2n^2}\right).
\]
\(- \frac{1}{4}\)
\( 1\)
\( 0\)
\( \infty \)
2010005308
Level:
C
Find the following limit.
\[
\lim\limits_{n\to\infty} \left( \frac{1+2+3+\dots+n}{4n^2-3}\right)
\]
\( \frac{1}{8}\)
\( \frac{1}{4}\)
\( 0\)
\( \infty \)
2010005307
Level:
C
Find the limit.
\[
\lim\limits_{n\to\infty}\frac{3+\frac32+\frac34+\dots+\frac3{2^n}}{2+\frac23+\frac29+\dots+\frac2{3^n}}
\]
\( 2 \)
\( \frac32 \)
\( 0 \)
\( \infty \)
\( \frac23 \)
2010005306
Level:
C
Find the limit.
\[
\lim\limits_{n\to\infty}\left(10^{-1} + 10^{-2} + \dots + 10^{-n} \right)
\]
\( \frac19 \)
\( \frac{1}{10} \)
\( \frac{9}{10} \)
\( 0 \)
\( \infty \)
2010005305
Level:
C
Find the limit.
\[
\lim\limits_{n\to\infty}\frac{\sqrt{6n^3-3n+2}}{\sqrt{2n^3+3n-6}}
\]
\( \sqrt3 \)
\( -\frac13 \)
\( 3 \)
\( 0 \)
\( \infty \)