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A sequence is defined by \(a_0 = 0\) and \(a_{n + 1} = \dfrac{1}{a_n + 1}\)

 

What values does \(a_n\) approach as n becomes large?

 Jul 2, 2020
 #1
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a(n) approaches 0.

I just plugged in a couple of values and it led to a pattern. For example, plug in 0 to n, and using the fact that a(0)=0, you will get a(1)=1. Then plug in 1 to n, and you will get a(2)=1/2. This will be an infinite series, and for every consecutive term, the result will be divided by 2.

1, 1/2, 1/4, 1/8, ... , 1/2^(n)

 

- hellospeedmind

 Jul 2, 2020

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