题目
题目

MTH1030 -1035 - S1 2025 MTH1030/5 Week 8 lesson quiz: Infinite sequences and series

简答题

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?

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标准答案
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思路分析
We are asked to determine how many of the given sequences are divergent among five labelled sequences a) through e). Option a) a) 1, -1, 1/2, -1/2, 1/3, -1/3, ... - The absolute values follow 1, 1, 1/2, 1/2, 1/3, 1/3, ... which tend to 0 as n grows, and the sign......Login to view full explanation

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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.

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