Hello community. I'm asked to show that if 1 < uk then (u-1/k)^n is greater or equal to u^n - (u^(n-1))*n/k. I'm supposed to use Bernoulli's inequality. I'd appreciate any hint. Please don't solve it for me
I have found a counter-example, taking u = -7, k = -1/3 and n = 3. Apparently the author of the book from which I took the exercise meant 1 < u and 1 < k or maybe 1 < uk with the condition that both be positive. I had to go back to the text where he proves the existence of the positive nth root of c > 0, there he uses that inequality (which was giving me a headache already) in a crucial step but he's only working with positive numbers, then he asks one to prove it as an exercise later. So if we attach to standard notation, that meaning:"1 < uk" means the product of u and k is greater than one, he's basically telling you to prove something false.