Question

giúp mk nha mn

cảm ơn mn

chứng minh: 1/2 + 1/3 + ... + 1/16 ko phải là số tự nhiên

Answer 1

Ta có:

A = (1/2 + 1/3 + 1/4 + 1/5) + (1/6 + 1/7 + 1/8) + (1/9 + 1/10 + 1/11) + (1/12 + 1/13 + 1/14) + (1/15 + 1/16 + 1/17) <

(1/2 + 1/3 + 1/4 + 1/5) + 3(1/6) + 3(1/9) + 3(1/12) + 3(1/15)

= 2(1/2 + 1/3 + 1/4 + 1/5)

< 2(1/2 + 1/2 + 1/4 + 1/4) = 3

Mặt khác A = (1/2 + 1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) + (1/9 + 1/10 + 1/11 + 1/12) + (1/13 + 1/14 + 1/15 + 1/16) + 1/17

> (1/2 + 1/3 + 1/4) + 4(1/8) + 4(1/12) + 4(1/16)

=2(1/2 + 1/3 + 1/4) > 2(1/2 + 1/4 + 1/4) = 2

=> 2 < A < 3 

=> ko la số tự nhiên