Find the sequence A1 = 1 an + 1 = (2An) / (2 + an) find the general term formula and prove it by mathematical induction
an+1=2an/(2+an)
1/an+1=(2+an)/2an=1/an+1/2
1/an+1-1/an=1/2
1 / an is an arithmetic sequence with initial value of 1 and difference of 1 / 2
So, 1 / an = (1 + n) / 2
an=2/(1+n)
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