Series are an important part of Calculus. In this next series of blog posts, I will be discussing infinite series and how to determine if they converge or diverge. For a refresher: A series is the sum of a list of terms that are generated with a pattern. A series is denoted with a ...
Answer to: Does the series diverge or converge. \sum_{k=1}^{\infty} \frac{g^k}{10^{k-3}} By signing up, you'll get thousands of step-by-step...
cos^2(n)总是小于1的 所以分子总是小于sqrt(n)的。分母则是n的平方量级，那个-2在n比较大时可忽略不计。所以整个式子的量级是n的-3/2次幂，比调和级数小多了，converge.
Determine if the following series converge or diverge: (a) \displaystyle \sum_{n \ = \ 3}^{\infty} (-1)^{n+1} \frac{n - 2}{n^{2} + 3n} (b) \displaystyle \sum_{n \ = \ 1}^{\infty} \frac{n^{2} + 3}{\sq Determine whether the following series ...
alternating series test converge (2 parts) 1) when the n+1 term < nth term2) the limit as n --> ∞ is equal to 0 ratio test converge the limit as n --> ∞ of the absolute value of the a(n+1) / a(n) is LESS than one ratio test diverge the limit as n --> ∞ of the...
To know how to find the sum of a series in geometric progression, we can use either the finite sum formula or the infinite sum calculation. A geometric series can converge or diverge depending on the value of the common ratio rr. To decide on the convergence vs. divergence of a geometric...
Does the series converge or diverge? Give reason for you answer ∑n=1∞−2nn Mathematical Series: For the series that has the nth term such that the power in the denominator is greater than 1, then such series will converge, according to p-test criteria. We may a...
Determine whether the following series converge or diverge using the Comparison Test or Limit Comparison Test.∑_(n=1)^∞(1)/(√[n](n+1)(n-1)) 相关知识点: 试题来源: 解析 1/(√[3](n(n+1)(n-1)))=1/(3n^(n-n))1/(√[3](n^3)) 1 7 √[3](n(n+1)(n-1))1/n ...
Does the series 1+ 1(2^3)+ 1(3^3)+⋯ + 1(n^3)+⋯ converge or diverge? 相关知识点: 试题来源: 解析 converges by the p-Series Test.结果一 题目 Does the series converge or diverge? 答案 converges 结果二 题目 Does the series converge or diverge? 答案 Converges because p...
using the ratio test, determine if the following series converge or diverge: \sum_{n = 0 }^{\infty } \frac{((3^n)(n!)((n+1)!)((n+2)!)))}{((3n)!)} Use the ratio test to determine whether the following s...