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`49/543``8/89``1/52`non of these

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ASolution :

Let f (n)=`a_n=(n^2)/(n^3 + 200),n in N`.<br> `f(n)=(2(n^3+200)n-3n^4)/(n^3+200)=n(400-n^3)/(n^3+200)^2` <br> <br> Clearly f'(n) `ne ` 0 for any n `in ` N .So f(n) has no extreme point <br> But <br> `f(n) gt 0 " for " n le 7` and decresing for `n le 8` <br> Now `f(7)=(49)/(543) and f(8)=(8)/(89)` <br> Clearly , `f(7) gt f(8)` <br> Hence , the value of the largest term is `49/543`