let-give-u-n-k-1-n-1-k-ln-n-1-prove-that-u-n-is-convergent-2-if-lim-n-u-n-prove-the-0-lt-lt-1-

Question Number 31417 by abdo imad last updated on 08/Mar/18

l e t g i v e u_{n} = \sum_{k = 1}^{n} \frac{1}{k} - l n (n)

1) p r o v e t h a t u_{n} i s c o n v e r g e n t

2) i f γ = {l i m}_{n \to \infty} u_{n} p r o v e t h e 0 < γ < 1 .