Choose the correct answer.

Given the integers r > 1, n > 2, and coefficients of (3r)^th and (r + 2)^nd terms in the binomial expansion of (1 + x)²ⁿ are equal, then:

Question

Choose the correct answer. Given the integers r > 1, n > 2, and coefficients of (3r) th and (r + 2) nd terms in the binomial expansion of (1 + x) 2n are equal, then:

Aicharya · Accepted Answer

Solution: The given expression is $(1 + \text{x})^{2\text{n}}$ $\therefore\text{T}_{3\text{r}}=\text{T}_{(3\text{r}-1)+1}=\ ^{2\text{n}}\text{C}_{3\text{r}-1}\ \text{x}^{3\text{r}-1}$ and $\text{T}_{\text{r}+2}=\text{T}_{(\text{r}+1)+1}=\ ^{2\text{n}}\text{C}_{\text{r}+1}\text{x}^{\text{r}+1}$ Given, $^{2\text{n}}\text{C}_{3\text{r}-1}=\ ^{2\text{n}}\text{C}_{\text{r}+1}$ $\Rightarrow3\text{r}-1+\text{r}+1=2\text{n}\ \ [\because\ ^\text{n}\text{C}_\text{x}=\ ^\text{n}\text{C}_\text{y}\Rightarrow\text{x}+\text{y}=\text{n}]$ $\therefore\text{n}=2\text{r}$

Choose the correct answer. Given the integers r &gt; 1, n &gt; 2, and coefficients of (3r) th and (r + 2) nd…

Solution

Choose the correct answer. Given the integers r > 1, n > 2, and coefficients of (3r) th and (r + 2) nd…