Let-s-n-c-1-1-1-2-n-c-2-1-1-2-1-3-n-c-3-1-n-1-1-1-2-1-3-1-n-n-c-n-then-prove-that-s-n-1-

Question Number 29196 by mathshooter last updated on 05/Feb/18

Let s = n_{c_{1}} - (1 + \frac{1}{2}) n_{c_{2}} + (1 + \frac{1}{2} + \frac{1}{3}) n_{c_{3}}

+ \dots \dots . + {(- 1)}^{n - 1} (1 + \frac{1}{2} + \frac{1}{3} + \dots . + \frac{1}{n}) n_{c_{n}}

then prove that s \times n = 1 .