题目
题目
简答题

Define a sequence of numbers like this: x1=π;xn+1=xn−(the nth digit of π)∗10−n[math]x_1=\pi; x_{n+1}=x_n-(\mbox{the nth digit of } \pi)*10^{-n}. Here the 1st digit of π[math]\pi is 1, the second 4, etc. Is this sequence convergent? If it is convergent, what is its limit? Give your answer no or enter the limit.

查看解析

查看解析

标准答案
Please login to view
思路分析
The problem defines a sequence by x1 = π and x_{n+1} = x_n − (the nth digit of π) × 10^{−n}, where the nth digit of π refers to the decimal digits 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, … in order. To unders......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

Here are a some sequences of numbers:a) \(1, -1, 1/2, -1/2, 1/3, -1/3, \ldots\)b) \(1, -2, 3, -4, 5, -6, …\)c) \(0, 0, 0, 0, 0, …\)d) \(1, 2, 3, 4, 5, 6, …\)e) \(0+1, 1+1/2, 0+1/3, 1+1/4, 0+1/5, 1+1/6, ….\)How many of these sequences are divergent?

Here are a some sequences of numbers:a) [math: 1,−1,1/2,−1/2,1/3,−1/3,…]1, -1, 1/2, -1/2, 1/3, -1/3, \ldotsb) [math: 1,−2,3,−4,5,−6,…]1, -2, 3, -4, 5, -6, …c) [math: 0,0,0,0,0,…]0, 0, 0, 0, 0, …d) [math: 1,2,3,4,5,6,…]1, 2, 3, 4, 5, 6, …e) [math: 0+1,1+1/2,0+1/3,1+1/4,0+1/5,1+1/6,….]0+1, 1+1/2, 0+1/3, 1+1/4, 0+1/5, 1+1/6, ….How many of these sequences are divergent?

Let  { 𝑎 𝑛 } 𝑛 = 0 ∞  be a POSITIVE sequence.  Which of the following statements must be true? Select all the correct answers. 

Let  { 𝑎 𝑛 } 𝑛 = 0 ∞ be a sequence. Let 𝐿 ∈ 𝑅   . Which statements are equivalent to " { 𝑎 𝑛 } 𝑛 = 0 ∞ → 𝐿 " ? Select all the correct answers.

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！