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Limits Continuity and Differentiability question

2022 · Shift 2 · Q36

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2022 · Shift 2 · Q36

Limits Continuity and Differentiability question

2022 · Shift 2 · Q36

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMCQ+3 / −1

For positive integer

n

, define

f(n)=n+\frac{16+5 n-3 n^{2}}{4 n+3 n^{2}}+\frac{32+n-3 n^{2}}{8 n+3 n^{2}}+\frac{48-3 n-3 n^{2}}{12 n+3 n^{2}}+\cdots+\frac{25 n-7 n^{2}}{7 n^{2}} .

Then, the value of

\mathop {\lim }\limits_{n \to \infty } f\left( n \right)

is equal to :

A
$3+\frac{4}{3} \log _{e} 7$
B
$4-\frac{3}{4} \log _{e}\left(\frac{7}{3}\right)$
C
$4-\frac{4}{3} \log _{e}\left(\frac{7}{3}\right)$
D
$3+\frac{3}{4} \log _{e} 7$

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