JEE Mains · Maths · STD 11 - 7. binomial theoram
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 \(138\)
- D \(118\)
Answer & Solution
Correct Answer
(D) \(118\)
Step-by-step Solution
Detailed explanation
\({ }^{ n } C _{ r -1}:{ }^{ n } C _{ r }:{ }^{ n } C _{ r +1}=2: 5: 12\) 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)\(\&(2)\)…
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