Question

If coefficients of $( - 1)^{n}$ term and $n + 1$ term are equal in the expansion of $y = 3x + 6x^{2} + 10x^{3} + ....,$ then the value of r will be.

• A. 14
• B. 15
• C. 13
• D. 16

Answer 1

Answer: (A)

14

Answer 2

Coefficient of $(1 + x)^{20}$ term in expansion of

(1 + x)⁴³ = $r^{th}$ and coefficient of $(a + 2x)^{n}$ term

= coefficient of $\frac{n(n + 1)....(n - r + 1)}{r!}a^{n - r + 1}(2x)^{r}$ term = $\frac{n(n - 1)....(n - r + 2)}{(r - 1)!}a^{n - r + 1}(2x)^{r - 1}$

According to question $\frac{n(n + 1)....(n - r)}{(r + 1)!}a^{n - r}(x)^{r}$ $16^{th}$

then $(\sqrt{x} - \sqrt{y})^{17}$or $136xy^{7}$ or $136xy$.