Choose the correct answer.

If A and B are coefficient of xⁿ in the expansions of (1 + x)²ⁿ and (1 + x)^{2n – 1} respectively, then $\frac{\text{A}}{\text{B}}$ equals:

Hint: $\frac{\text{A}}{\text{B}}=\frac{^{2\text{n}}\text{C}_\text{n}}{^{2\text{n}-1}\text{C}_\text{n}}=2$

Question

Choose the correct answer.

If A and B are coefficient of xⁿ in the expansions of (1 + x)²ⁿ and (1 + x)^{2n – 1} respectively, then $\frac{\text{A}}{\text{B}}$ equals:

Hint: $\frac{\text{A}}{\text{B}}=\frac{^{2\text{n}}\text{C}_\text{n}}{^{2\text{n}-1}\text{C}_\text{n}}=2$

Aicharya · Accepted Answer

Solution: Given expression is (1 + x) 2n $\text{T}_{\text{r}+1}=\ ^{2\text{n}}\text{C}_\text{r}\text{x}^\text{r}$ $\therefore$ Coefficient of xn = 2n C n = A (Given) In the expression of (1 + x) 2n - 1 $\text{T}_{\text{r}+1}=2^{\text{n}-1}\text{C}_\text{x}=\text{B}$ Given So, $\frac{\text{A}}{\text{B}}=\frac{^{2\text{n}}\text{C}_\text{n}}{^{2\text{n}-1}\text{C}_\text{n}}=\frac{^{2\text{n}}\text{C}_\text{n}}{^{2\text{n}-1}\text{C}_\text{n}}=\frac{2}{1}$ Hence, the correct option is (b).

Choose the correct answer. If A and B are coefficient of x n in the expansions of (1 + x) 2n and (1 + x) 2n…

Solution