Limit Rules for Sequences
Read this topicExplanations 2
- Suppose two (infinite) sequences a1,a2,a3,…a_1, a_2, a_3, \ldotsa1,a2,a3,… and b1,b2,b3,…b_1, b_2, b_3, \ldotsb1,b2,b3,… have limits aaa and bbb respectively. In other wor…
By Zilin Jiang, Po-Shen Loh, Felipe Vargas
- For the most part, the limit rules for functions carry over to sequences without a hitch.
By Victor Wang
Problems 5
- The sequence (xn)n≥1(x_n)_{n\ge1}(xn)n≥1 of reals satisfies limn→∞(x2n+x2n+1)=315\lim_{n\to\infty} (x_{2n} + x_{2n+1}) = 315limn→∞(x2n+x2n+1)=315 and limn→∞(x2n+x2n−1)=20…
- limn→∞(n2+3n−53n2−2n⋅12n3+2n2−7−n3−5n2−5n−4)=\lim_{n \to \infty} \left(\frac{n^2 + 3n - 5}{3n^2 - 2n} \cdot \frac{12n^3 + 2n^2 - 7}{-n^3 - 5n^2 - 5n - 4} \right) =n→∞lim(3n2−2…
- If an=3e−na_n = 3e^{-n}an=3e−n and bn=2n+12nb_n = \frac{2n+12}{n}bn=n2n+12, then what is limn→∞anbn\lim_{n \to \infty} a_nb_nlimn→∞anbn?
- Let two sequences ana_nan and bnb_nbn satisfy limn→∞an=2\lim_{n \to \infty} a_n = 2limn→∞an=2 and limn→∞bn=4\lim_{n \to \infty} b_n = 4limn→∞bn=4. What is the value of t…
- Fix a∈Ra \in \mathbb{R}a∈R and let ana_nan be a sequence such that limn→∞an=a\lim_{n \to \infty}a_n = alimn→∞an=a. Which of the following are true about limits of sequences?