Question

Solve $\underset{n\to \infty }{lim}\frac{(n+1{)}^2+5n}{n^2}$

• A. $\infty$
• B. $0$
• C. $1$
• D. $7$

Answer 1

The correct option is C $1$

We need to find value of limit ${lim}_{n\to \infty }\frac{{(n+1)}^2+5n}{n^2}$

Apply Fraction Rule $\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$

$={lim}_{n\to \infty }[\frac{{(n+1)}^2}{n^2}+\frac{5n}{n^2}]$

$={lim}_{n\to \infty }[{(1+\frac{1}{n})}^2+\frac{5n}{n}]$

Put the value $n=\infty$

$={(1+\frac{1}{\infty })}^2+\frac{5}{\infty }$

$=1$ ....As we know $\frac{1}{\infty }=0$