"If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1 + x)n + 5 are in the ratio 5 : 10 : 14, then the largest coefficient in this expansion is :"

Question

Accepted Answer

"Consider the three consecutive coefficients as

$^{n + 5}{C_r},{\,^{n + 5}}{C_{r + 1}},{\,^{n + 5}}{C_{r + 2}}$

$\because$ ${{^{n + 5}{C_r}} \over {^{n + 5}{C_{r + 1}}}} = {1 \over 2}$

$\Rightarrow {{r + 1} \over {n + 5 - r}} = {1 \over 2} \Rightarrow 3r = n + 3$ ...(i)

and ${{^{n + 5}{C_{r + 1}}} \over {^{n + 5}{C_{r + 2}}}} = {5 \over 7}$

$\Rightarrow$ $\Rightarrow {{r + 2} \over {n + 4 - r}} = {5 \over 7} \Rightarrow 12r = 5n + 6$ ...(ii)

From (i) and (ii) n = 6

Largest coefficient in the expansion is ${^{11}{C_6}}$ = 462"

If for some positive integer n, the coefficients
of three consecutive terms in the binomial
expansion of (1 + x)^{n + 5} are in the ratio
5 : 10 : 14, then the largest coefficient in this expansion is :

Solution

About this question

Drill 25 more like these. Every day. Free.

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of (1 + x)n + 5 are in the ratio 5 : 10 : 14, then the largest coefficient in this expansion is :

Solution

About this question

More Binomial Theorem questions

Drill 25 more like these. Every day. Free.

If for some positive integer n, the coefficients
of three consecutive terms in the binomial
expansion of (1 + x)^{n + 5} are in the ratio
5 : 10 : 14, then the largest coefficient in this expansion is :