12.Q. Let 0 < aı < bị and define az = Va,b , b2 Vanba , bat1 (a, + bi)/2, ..., Ant1 = (an + bn)/2, ... ove that a, < bq and, by induction, that an < bn. Show that the sequences ..it

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12.Q

12.Q. Let 0 < a, < bị and define
Va,bi, ba
(a, + b1)/2, ...
Ant1 = Vanbn , bn41
(an + bn)/2, ....
>
Prove that az < b2 and, by induction, that a, < bn. Show that the sequences
(an) and (bn) converge to the same limit.
Transcribed Image Text:12.Q. Let 0 < a, < bị and define Va,bi, ba (a, + b1)/2, ... Ant1 = Vanbn , bn41 (an + bn)/2, .... > Prove that az < b2 and, by induction, that a, < bn. Show that the sequences (an) and (bn) converge to the same limit.
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