Question

The sum of the first three coefficients in the expansion $(x+\frac{1}{y}{)}^n$ is 22. Then, the value of n is

• A. 8
• B. 7
• C. 6
• D. 5

Answer 1

Answer: (C)

6

Given that,

${n_C}_0+{n_C}_1+{n_C}_2=22$

$1+n+\frac{n(n-1)}{2}=22$

$2+2n+n^2-n=44$

$n^2+n-42=0$

$(n+7)(n-6)=0$

$n=-7$ or $n=6$

Hence, option C is correct.