The sequence {an} is defined by a1=2, and
an+1=12(an+2an),
for n⩾1. Assuming that {an} conver...
Mathematics, 27.11.2020 04:30 reecedstceklein
The sequence {an} is defined by a1=2, and
an+1=12(an+2an),
for n⩾1. Assuming that {an} converges, find its limit.
limn→∞an=
Hint: Let a=limn→∞an. Then, since an+1=1/2(an+2/an), we have a=1/2(a+2/a). Now solve for a
Answers: 1
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