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Prove by induction help.?
if sequence a_1=1 and a_n=3-(1/(a_n-1) for n greater than or equal to 2.
Prove by induction that {an} is an increasing sequence
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- ?Lv 75 years ago
Try telescoping
a_k+1 = 3 - 1/(a_k)
a_k = 3 - 1/(a_k-1)
a_k-1 = 3 - 1/(a_k-2)
(a_k+1) - a_(k-1) = (a_k+1 - a_k) + (a_k - a_k-1) = -1/(a_k) + 1/(a_k-2)
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