Proving a sequence is increasing

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I have a sequence which represents the values of the function (1 (x/n) )ⁿ n a natural number , I am asked to prove it is increasing by taking the quotient of u_(n 1) / u_(n). But only for n>|x|. I cant seem to prove the quotient is greater than one. I am supposed to use the Bernoulli inequality but I have been trying for several hours and not finding a solution. I tried to frame u_{n}(x) between 0 and 2ⁿ like so 0<(1 (1 (x/n) )ⁿ < 2ⁿ since -n<x<n and doing the same for u_{n 1} but it didn't work. Could someone help me find a solution, preferably using the Bernoulli inequality?

Thanks in advance

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WildFire814

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Posted: 5 years ago
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