Question

what is
$lim(n - > \infty ) \:\frac{(2n - 1) ^{2}}{n^{2} }$
​

Answer 1

ANSWER:

$\boxed{ \boxed{ \large{\bold{\lim_{n \to\infty}\:\frac{(2n - 1) ^{2}}{n^{2} } = 4}}}}$

GIVEN:

$\displaystyle \lim_{n \to\infty}\:\frac{(2n - 1) ^{2}}{n^{2} }$

TO FIND:

$The \: \: value \: \: of \: \displaystyle \lim_{n \to\infty}\:\frac{(2n - 1) ^{2}}{n^{2} }$

EXPLANATION:

$\displaystyle \lim_{n \to\infty}\:\frac{(2n - 1) ^{2}}{n^{2} }$

$\displaystyle \lim_{n \to\infty}\: \bigg({\frac{2n - 1}{n }} \bigg)^{2}$

$\displaystyle \lim_{n \to\infty}\: \bigg({\frac{2n}{n } - \frac{1}{n} } \bigg)^{2}$

$\displaystyle \lim_{n \to\infty}\: \bigg({\frac{2 \cancel{n}}{\cancel{n }} - \frac{1}{n} } \bigg)^{2}$

$\left(2 - \dfrac{1}{ \dfrac{1}{0} } \right)^{2}$

$\boxed{ \boxed{ \large {\bold{ \because \infty = \frac{1}{0} }}}}$

$\boxed{ \boxed{ \large {\bold{ \frac{1}{ \frac{1}{0} } = 0 }}}}$

${(2 - 0)}^{2}$

${2}^{2} = 4$

$\boxed{ \boxed{ \large{\bold{\lim_{n \to\infty}\:\frac{(2n - 1) ^{2}}{n^{2} } = 4}}}}$