If-n-gt-1-prove-by-mathematical-induction-that-n-n-1-1-n-1-lt-1-1-2-1-3-1-4-1-n-

Question Number 5513 by 314159 last updated on 17/May/16

I f n > 1, p r o v e b y m a t h e m a t i c a l i n d u c t i o n t h a t

n ({(n + 1)}^{\frac{1}{n}} - 1) < 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots \frac{1}{n} .