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

Answers (1)

\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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