题目
题目

MAT136H5 S 2025 - All Sections 5.2 preparation check

数值题

The series   converges to the number . (This is given information. You do not need to prove this, but we may be able to prove it before the end of the course.)  Compute    by adding the first several terms of the series. Notice that for each additional term you add, the sum is closer and closer to .   What is the smallest such that   gives an approximation of the number that is correct to 3 decimal places?   Side note: Some calculators do computations involving and many other transcendental numbers by using sums of series such as the one above (although recently there are also faster methods that calculators can use). 

查看解析

查看解析

标准答案
Please login to view
思路分析
The problem states that the infinite series converges to a certain number L (though L is not specified here), and asks for the smallest integer n such that the partial sum S_n approximates L to three decimal places. First, recall what it means to be correct to three decimal places: the approximation must be within 0.0005 of the true value L. That is, we require |S_n − L| < 0.0005. Next, we ......Login to view full explanation

登录即可查看完整答案

我们收录了全球超50000道考试原题与详细解析,现在登录,立即获得答案。

类似问题

Given the series    has infinite terms, what sum will this series approach but never reach? (type number only in box)

The infinite series \[1-1/2+1/2-1/3+1/3-\ldots\] converges. What is its sum?

Question text(1) Here is a convergent infinite series 1+1/2+1/4+1/8+1/16+...What kind of infinite series are we dealing with?Answer 1 Question 16[select: , arithmetic, geometric, p-series, harmonic, telescoping, none of the above]What is the fifth partial sum of this series (written in lowest terms)? Answer 2 Question 16[input] What's its sum? Answer 3 Question 16[input] (2). Here is another convergent infinite series 1+1/4+1/9+1/16+1/25+... What kind of infinite series are we dealing with?Answer 4 Question 16[select: , arithmetic, geometric, p-series, harmonic, telescoping, none of the above]What is the third partial sum of this series? Answer 5 Question 16[input] What is the integer part of its sum? Answer 6 Question 16[input] (3) Here is yet another converging infinite series What kind of infinite series are we dealing with?Answer 7 Question 16[select: , arithmetic, geometric, p-series, harmonic, telescoping, none of the above]What is the sum of the first three terms of this series? Answer 8 Question 16[input] What's its sum? Answer 9 Question 16[input] Check Question 16

Consider the series ∑ 𝑛 = 1 ∞ 0.01 . The terms are 𝑎 𝑛 = 0.01 .   a) Find the following partial sums: 𝑆 1 = [ Select ] 0.01 0.02 1 0 0.03 𝑆 2 =   [ Select ] 0.02 0.04 2 1 0.01 𝑆 3 = [ Select ] 3 4 0.03 0 0.01 𝑆 4 = [ Select ] 0.4 0.04 4 1 0.01   b) Find the limits:     lim 𝑘 → ∞ 𝑆 𝑘 =   [ Select ] infinity 0.04 0.01 negative infinity 0 and lim 𝑛 → ∞ 𝑎 𝑛 =   [ Select ] negative infinity infinity 0.01 1 0   c) Does the series ∑ 𝑛 = 1 ∞ 0.01  converge or diverge? [ Select ] The series converges There is not enough information to tell The series diverges   d) Suppose another series ∑ 𝑛 = 1 ∞ 𝑏 𝑛  has some unknown terms 𝑏 𝑛   but we know that lim 𝑛 → ∞ 𝑏 𝑛 = 0.01   (this means the numbers 𝑏 𝑛 are close to 0.01, but not necessarily equal to 0.01.)  What can be said about the convergence of the series ∑ 𝑛 = 1 ∞ 𝑏 𝑛  ? [ Select ] The series converges The series diverges There is not enough information to tell

更多留学生实用工具

加入我们，立即解锁 海量真题 与 独家解析，让复习快人一步！