The largest term in the sequence `a_n=(n^2)/(n^3+200)` is given by `(529)/(49)` (b) `8/(89)` `(49)/(543)` (d) none of these

Options

A. `(529)/(49)`
B. `(8)/(89)`
C. `(49)/(543)`
D. none of these

Answer

3

Explanation

Consider the function f(X)=`(x)^(2)/(x^(3)+200)`
`therefore f(X)=x(400-x^(3))/(x^(3)+200)^(2)=0`
`then x=(400)^(1//3)`
`x=(400)^(1//3)+h or f(X) lt0`
Thus f(x) has maxima at `x=(400^(1//3))`
Since `7 lt(400)^(1//3) lt 8` either `a_(7) or a_(8)` is the greatest term of the sequence .Therefore
`a_(7)=(49)/(543)` it the greatest term