题目 Determine whether the sequence converges or diverges. If it converges, find the limit. a_n=cos (2n) 相关知识点: 试题来源: 解析a_n=cos (2n). As n→ ∞, 2n→ 0, so cos (2n)→ cos 0=1 because cos is continuous. Converges....
Determine whether the sequence converges or diverges. If it converges, find the limit. a_n = 2n + 1/1 - 3Squarerootn Determine whether the sequence converges or diverges. If it converges, find the limit. a_n = (1 + \frac 5n)^n Determine whether the...
Determine whether the sequence converges or diverges: A_n = \frac{n!}{10^{6n Determine if the sequence converges or diverges an = (2n + 3)!/ (n + 1)! Determine whether the given sequence converges or diverges. {arctan ({2 n} / {2 n + 1})} Determine if the ...
back into the Calculus I material do some refreshing on limits at infinity as well at L'Hospital's rule.Calculus II - Solutions to Practice ProblemsStep 2We can see that the limit of the terms existed and was a finite number and so we know that the sequence converges and its limit is ...
Determine whether the sequence converges or diverges by finding the limit. b_n = ((-1)^n (2n + 1))/(3n + 2) Determine the given sequence converges or diverges; find its value if converges. a_n = (-1)^n 8 / n Determine whether the sequence con...
State whether the sequence converges or diverges. If the sequence converges, find its limit. an={(1+3n)n} Limits: We have an undefined limit in the form of zero to the power infinity. We can calculate it by taking the log and using the L'Hospital's Rule or ...
converges to 0BF(n)=(n+1)n limlimits_(n→∞)a_n=limlimits_(n→∞)(n+1)n =1converges to 1C:F(n)=2^n limlimits_(n→∞)a_n=limlimits_(n→∞)2^n =∞DivergesD:f(n)=(-1)^nlimlimits_(n→∞)a_n=limlimits_(n→∞)(-1)^n The anwser will always -1 or 1 Diverges...
6. Determine whether {2nn!}∞n=0{2nn!}n=0∞ converges or diverges. If it converges, compute the limit.Solution: an+1an=2n+1(n+1)!2nn!=2n+1<1an+1an=2n+1(n+1)!2nn!=2n+1<1 when n>2n>2. Thus it is decreasing. On the other hand, 2...
How do you tell if a series converges or diverges? convergeIf a series has a limit, and the limit exists, the series converges. divergentIf a series does not have a limit, or the limit is infinity, then the series is divergent. divergesIf a series does not have a limit, or the limi...
(类似极限定义)如果对于所有 ϵ>0 都有对应的 N, 使得对于所有 N>n 情况时,有 |an−L|<ϵ, 则称数列 {an} 收敛(converges),否则 {an} 发散(diverges)。当 {an} 收敛时,记为 limn→∞an=L 或者干脆 an→L. 其中L 是数列 {an} 的极限(limit)。 如果{an} 对于每一个 M 都有一个 N, ...