1-1/6=5/6;1-1/7=6/7;........(1-(1/n+4))=(n+3)/(n+4);(1-(1/n+5))=(n+4)/(n+5); there fore (5/6)(6/7)........((n+3)/(n+4))((n+4)/(n+5))=5/(n+5)=1-(n/(n+5))

Take n=5 for example, then above equation becomes 5/6*6/7*7/8*8/9*9/10=5/10.
Which implies all the term cancel except first numerator and last denominator, so in general 5/n+5
is the answer.

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