Would someone mind showing me how to do this proof?
Use Bernoulli's inequality to show that (1 + (1/n))^n < (1 + (1/(n+1)))^(n+1) for all n in N.
I'm given a hint of let x = -1/(n+1)^2.
Thank you in advance.
Yeah, sorry for the confusion. I meant the original inequality (the one proven using Bernoulli's Inequality). This one:
(1 + (1/n))^n < (1 + (1/(n+1)))^(n+1) for all n in N.
This is just a hint for how to attack the problem as given in the textbook.
Use x1 = 1, xk = (1 + (1/n)), and k = 2,3,...,n+1.