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I have been over this problem for a long time now and I just can't figure the way out.

$$\lim_{x\to \infty} ((1.5^x + ([(1+ 0.0001)^{10000}])^x)^{1/x}$$ where [.] represents greatest integer function

From Binomial theorem, it is evident to me that I can write the sequence as $$ \lim_{x\to \infty} ((1.5^x + (2)^x)^{1/x}$$

I am completely stuck over this step and don't know how to move ahead.

P.S. Wolfram shows that the answer is $2$ but I just don't know how to calculate it.

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    Did you mean $[(1+ 0.0001)^{10000}]$ because $[1+ 0.0001]^{10000}=1^{10000}$ – 2017-01-15
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    Ya, just give me a second to edit it. – 2017-01-15
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    $\lim_{x\to \infty} ((1.5^x + (2)^x)^{1/x}=2\lim_{x\to \infty} (((\frac{3}{4})^x +1)^{1/x}$ – 2017-01-15

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