# Sequence converges

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Show that the sequence defined by y1=1 and y_n+1=4-1/y_n converges and find the limit

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:04 pm ad1c9bdddfhttps://brainmass.com/math/real-analysis/sequence-converges-25527

#### Solution Preview

First, we want to prove 0 < y_n < 4 for all n by induction,

1)For n=1, 0<y1<4 is obvious

2) secondly assume 0 < y_n < 4 for general, then 0< 1/y_n <1/4

( -1/4 < -1/y_n < 0) , and therefore 0 < 4-1/y_n < 4, which ...

#### Solution Summary

This shows how to find the limit of a converging sequence

$2.49