- #1
Maddiefayee
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Homework Statement
For some background, this is an advanced calculus 1 course. This was an assignment from a quiz back early in the semester. Any hints or a similar problem to guide me through this is greatly appreciated! Here is the problem:
Find a convergent subsequence of the sequence:
{(-1)n (1-(1/n)}∞n=1
Homework Equations
I don't think there are any equations needed. The class is all about proofs. Here's a definition:
A sequence {an} is said to converge to the number a provided that for every positive number ε there is an index N such that:
|an - a| < ε , for all indices of n ≥ N
The Attempt at a Solution
So this was my attempt. My "solution" was: {(1/n2)(-1)n}10n=2
How I got to this solution was honestly listing out a few terms of the original sequence and then finding another sequence that I thought would make sense.
Here's the note from my professor: "Sequences, and subsequences, have an infinite number of terms. Also, this sequence is not a subsequence."