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a_{n+1} =\frac{a_n}{1+a_n} , a_0 =\alpha > 0 , a_n wanted

Source: ITAMO 1986 p2

February 2, 2020

recurrence relationSequencealgebra

Problem Statement

Determine the general term of the sequence (

a_n

) given by

a_0 =\alpha > 0

and

a_{n+1} =\frac{a_n}{1+a_n}