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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

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Solution Summary

This shows how to find the limit of a converging sequence

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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 ...

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