[High-School] Proving a sequence is increasing after some number n.

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So I have a geometric sequence as a function of x (real number) defined as (1 x/n)ⁿ . I am asked to prove it is increasing for n>|x|. I tried to frame the sequence between 0 and 2ⁿ since -n<x<n. But I couldn't make it work beyond that.

Also, the question states I should use the Bernoulli inequality by manipulating the quotient of u_{n 1} and u_{n} and eventually proving it is greater than 1. However, I've been trying for several hours and just can't make it work.

I would appreciate if if someone could give me a hint on how to approach a problem like that. I am finding it very challenging to "see the picture".

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WildFire814

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Posted: 5 years ago
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