# For a positive integer n, $\left ( 1+\frac{1}{x} \right )^{n}$ is expanded in increasing power of x, if three consecutive coefficient in this expansion are in the ratio $2:5:12$, then n is equal to = ______ Option: 1 124 Option: 2 120 Option: 3 118 Option: 4 120

$\frac{^nC_{r-1}}{^nC_r}=\frac{12}{5}$

$\frac{r}{n-r+1}=\frac{12}{5}---(i)$

$\\\frac{^nC_{r}}{^nC_{r+1}}=\frac{5}{2} ....(ii)\\ \frac{r+1}{n-r}=\frac{5}{2}$

From euqation (i) and (ii)

n = 118

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