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  • Evaluate   <img alt="\mathrm{ =\lim _{n \rightarrow \infty}\left(\lim _{k \rightarrow \infty}\left(\frac{1}{1+2^{n-k}}\right)\right) }" src="https://entrancecorner.oncodecogs.com/gif.late

Evaluate   \mathrm{ =\lim _{n \rightarrow \infty}\left(\lim _{k \rightarrow \infty}\left(\frac{1}{1+2^{n-k}}\right)\right) }

Option: 1

1


Option: 2

0


Option: 3

-1


Option: 4

3


Answers (1)

As the inner limit doesn't depend on n you can rewrite it as:
                   

                                     \mathrm{ \lim _{n \rightarrow \infty}\left(2^{-n} \lim _{k \rightarrow \infty} \frac{1}{2^{-n}+2^{-k}}\right) }

The inner limit is then just \mathrm{\frac{1}{2^{-n}}} which would cancel giving you
                                   

                                                        \mathrm{ \lim _{n \rightarrow \infty} 1=1 }

Posted by

Kshitij

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