- #1

jimmypoopins

- 65

- 0

## Homework Statement

Show that the sequence defined by y_1=1 and y_n+1 = 4-(1/y_n) converges and find the limit.

## Homework Equations

thm: a sequence that is monotone and bounded is convergent.

## The Attempt at a Solution

i used induction to show that the sequence is increasing and bounded above by 4, so i showed that it is convergent.

i'm having issues showing mathematically that the limit is 4. maybe I'm forgetting something from calc 2?

the book suggests to "take the limit of each side of the recursive equation to explicitly compute lim y_n," but i don't understand how to do that.

any help in the right direction would be gratefully appreciated :)