MCQ
For a positive integer $n,\left(1+\frac{1}{x}\right)^{n}$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are in the ratio, $2: 5: 12,$ then $n$ is equal to
- A$115$
- B$128$
- C$138$
- ✓$118$
Now $\frac{{ }^{n} C_{r-1}}{{ }^{n} C_{r}}=\frac{2}{5}$
$\Rightarrow 7 r=2 n+2$
$\frac{{ }^{n} C_{r}}{{ }^{n} C_{r+1}}=\frac{5}{12}$
$\Rightarrow 17 r =5 n -12$
On solving (1)$\&(2)$
$\Rightarrow n =118$
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