Convergence Problem

Donalbain47 · **Joined:** Fri, 29 Jan 2016 16:55:04 UTC **Posts:** 28

The text has: "Let (aₙ) be the sequence where a₁ = 0.1, a₂ = 0.12, a₃ = 0.123, a₄ = 0.1234, and so on."

Later the text has: "Furthermore note that since all the terms begin with 0.1, we have that aₙ ≤ 1 for all n."

I understand why 1 is an upper boundary, but I don't understand how the sequence can ever be equal to it. And there are plenty of upper boundaries that are lower than it -- this sequence will never exceed .2, .3, .4, etc. So, I do not understand the ≤ here. Why not just <?

helmut · **Posted:** Tue, 19 Oct 2021 16:02:04 UTC

What you are saying is correct, a_n<1

for all n. But $a_n\leq 1$ is of course also correct.

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Convergence Problem

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