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Question Number 5809 by Apoorva last updated on 28/May/16

Commented by Apoorva last updated on 28/May/16

$$pleasesolvethislimit$$

Answered by Yozzii last updated on 28/May/16

$$\underset{n\to \mathrm{\infty }}{\lim }\frac{{(2n+1)}^4-{(n-1)}^4}{{(2n+1)}^4+{(n-1)}^4}=l$$$$l=\underset{n\to \mathrm{\infty }}{\lim }\frac{1-{\left(\frac{n-1}{2n+1}\right)}^4}{1+{\left(\frac{n-1}{2n+1}\right)}^4}$$$$l=\underset{n\to \mathrm{\infty }}{\lim }\frac{1-{\left(\frac{1-\frac{1}{n}}{2+\frac{1}{n}}\right)}^4}{1+{\left(\frac{1-n^{-1}}{2+n^{-1}}\right)}^4}$$$$l=\frac{1-{\left(\frac{1-0}{2+0}\right)}^4}{1+{\left(\frac{1-0}{2+0}\right)}^4}$$$$l=\frac{1-\frac{1}{16}}{1+\frac{1}{16}}$$$$l=\frac{15}{17}$$

Commented by Apoorva last updated on 29/May/16

$$Thankyou$$

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