Question

Which of the following can be a value of n if the expression of$(x+\frac{1}{x^2})^n$ has a term independent of x ?

• A. 4
• B. 6
• C. 7
• D. 8

Answer 1

Answer:

B. 6

Term independent of x in $(a+b)^n$

$T_{r+1}=^nC_ra^{n-r}b^r$

$T_{r+1}=^nC_rx^{n-r}(\frac{1}{x^2})^r$

$^nC_rx^{n-r}(\frac{1}{x^2})^r=^nC_rx^{n-r}(x^{-2})^r$

$=^nC_rx^{n-r}\times x^{-2r}$

$-^nC_rx^{n-r-2r}$

$=^nC_rx^{n-3r}$

$x^0=x^{n-3r}$

$0=n-3r$

$3r=n$

$=6$