- #1

Shackleford

- 1,661

- 2

I know the Cauchy criterion for a convergent sequence. A Cauchy sequence is one in which the distance between successive terms becomes smaller and smaller. You can find a number N such that the terms after that, pairwise, have a a distance that is less than epsilon.

After looking at an example in the book, I was able to write this down. It would appear that the sequence converges to zero since the numerator is bounded by -1 and 1. It looks like the Cauchy criterion for convergent series is satisfied too since you can make m and n and a function of epsilon. However, I'm not too sure about my work.

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-1.png

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20111116_173313.jpg [Broken]

After looking at an example in the book, I was able to write this down. It would appear that the sequence converges to zero since the numerator is bounded by -1 and 1. It looks like the Cauchy criterion for convergent series is satisfied too since you can make m and n and a function of epsilon. However, I'm not too sure about my work.

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-1.png

http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20111116_173313.jpg [Broken]

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