Find a formula for sn, n≥1, if sn is given by 3/5,4/8,5/11,6/14,7/17,…

s1=(2+n)/[2*(2+n)+(n-2)]
s2=(2+2)/[2*(2+2)+(2-2)]
s3=(2+3)/[2*(2+3)+(3-2)]
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sn=(2+n)/[2*(2+n)+(n-2)]