2010005301
Level:
C
Consider the sequence
\[
\left (2+\frac{(-1)^{n}}
{2n}\right )_{n=1}^{\infty }
\]
and its limit \(L\). How many terms
of the sequence differ from \(L\)
by more than \(\frac{1}
{100}\)?
\(49\)
\(50\)
\(10\)
\(100\)
Limit of a sequence
Limits of Sequences - Mix II
Submitted by ladislav.foltyn on Tue, 05/28/2019 - 10:13Limits of Sequences II
Submitted by ladislav.foltyn on Tue, 05/28/2019 - 09:47Question:
For each given limit of a sequence decide whether its value is $0$, $\infty$, $-\infty$, $1$, or $-1$.
Limits of Rational Sequences II
Submitted by ladislav.foltyn on Tue, 05/28/2019 - 09:29Rational Sequences Involving Exponentials
Submitted by ladislav.foltyn on Thu, 05/02/2019 - 13:41Rational Sequences
Submitted by ladislav.foltyn on Mon, 03/04/2019 - 19:38Question:
Given the limits of sequences, decide for each limit whether its value is $0$, $\infty$, $-\infty$ or a real number $k$, $k\neq0$.
1003047310
Level:
A
Find the limit.
\[ \lim\limits_{n\to\infty}\frac{-4n+5}{2n+2} \]
\( -2 \)
\( 0 \)
\( \infty \)
\( -\infty \)
\( \frac52 \)
1003047309
Level:
A
The sequence
\[ \left(\frac{3n^5+2n^3+1}{n^3+3}\right)_{n=1}^{\infty} \]
is divergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=\infty \).
is convergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=0 \).
is convergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=3 \).
is divergent and \( \lim\limits_{n\to\infty}\frac{3n^5+2n^3+1}{n^3+3}=-\infty \).
has no limit.
1003047308
Level:
A
Choose the best first step to take in order to evaluate the limit of the following sequence.
\[ \left(\frac{3n^2-2n+4}{8n^2+13n+2}\right)_{n=1}^{\infty} \]
We divide the numerator and the denominator by \( n^2 \).
We divide the numerator and the denominator by \( n \).
We substitute \( n=\infty \).
We factor out \( n \) in the numerator and in the denominator separately.
We factor out \( 8 \) in the numerator and in the denominator separately.
1003047307
Level:
A
Find the limit.
\[ \lim\limits_{n\to\infty}\frac{4n^2+n-2}{-5n^2-3n} \]
\( -\frac45 \)
\( 0 \)
\( \infty \)
\( -\infty \)
\( \frac45 \)