"For a positive integer n, ${\left( {1 + {1 \over x}} \right)^n}$ 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________."

Question

Accepted Answer

"Let, three consecutive coefficients are

${}^n{C_{r - 1}},{}^n{C_r},{}^n{C_{r + 1}}$

${}^n{C_{r - 1}}:{}^n{C_r}:{}^n{C_{r + 1}} = 2:5:12$

Now, ${{{}^n{C_{r - 1}}} \over {{}^n{C_r}}} = {2 \over 5}$

$\Rightarrow 7r = 2n + 2$ ...(i)

${{{}^n{C_r}} \over {{}^n{C_{r + 1}}}} = {5 \over {12}}$

$\Rightarrow 7r = 5n - 12$ ...(ii)

On solving (i) and (ii) we get n = 118 "

For a positive integer n,
${\left( {1 + {1 \over x}} \right)^n}$ 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________.

Solution

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For a positive integer n, ${\left( {1 + {1 \over x}} \right)^n}$ 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________.

Solution

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More Binomial Theorem questions

Drill 25 more like these. Every day. Free.

For a positive integer n,
${\left( {1 + {1 \over x}} \right)^n}$ 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________.