Question

The value of $\underset{x\to \infty }{lim}\frac{(x+1{)}^{10}+(x+3{)}^{10}+(x+5{)}^{10}+\cdots +(x+49{)}^{10}}{(x+2{)}^{10}+(x+4{)}^{10}+(x+6{)}^{10}+\cdots +(x+26{)}^{10}}$ is

• A. $\frac{24}{13}$
• B. $\frac{49}{26}$
• C. $2$
• D. $\frac{25}{13}$

Answer 1

The correct option is D $\frac{25}{13}$

$L=\underset{x\to \infty }{lim}\frac{(x+1{)}^{10}+(x+3{)}^{10}+\cdots +(x+49{)}^{10}}{(x+2{)}^{10}+(x+4{)}^{10}+\cdots \cdot (x+26{)}^{10}}$

$\because$ Degree of Numerator $=$ Degree of Denominator $=10$
$\therefore L=\frac{\text{coefficient of}{x}^{10}\text{in Numerator}}{\text{coefficient of}{x}^{10}\text{in Denominator}}=\frac{25}{13}$