- #1

Maddiefayee

- 5

- 0

## 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 {a

_{n}} is said to converge to the number a provided that for every positive number ε there is an index N such that:

|a

_{n}- a| < ε , for all indices of n ≥ N

## The Attempt at a Solution

So this was my attempt. My "solution" was: {(1/n

^{2})(-1)

^{n}}

^{10}

_{n=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."