Evaluate lim Here [.] denotes the greatest integer function.
My Try : I know how to solve this kind of problem :\lim_{n \to \infty} ((a)^n +(b)^n)^{\frac{1}{n}} where a, b \geq 0. But here I can not find ([(1+0.0001)^{10000}])?
Can anyone please help me out?
Thank You.
Answer
Since for all n\in \mathbb{N}
2\le\left(1+\frac{1}{n}\right)^n \le e < 3
we have that
\left((15)^n +\left[\left(1+\frac1{10000}\right)^{10000}\right]^n\right)^{\frac{1}{n}}= \left((15)^n +2^n\right)^{\frac{1}{n}}=15 \left(1 +(2/15)^n\right)^{\frac{1}{n}}\to 15
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