Question

Chứng tỏ rằng:

a ) 1 1.2   + 1 2.3   + ... + 1 9.10 < 1   b ) 3 2.5   + 3 5.8   + 3 8.11   + 3 11.14   + 3 14.17 + 3 17.20 < 1 2   c ) 1 2 2   + 1 3 2   + 1 4 2   + ... + 1 25 2   < 1  

Answer 1

a ) 1 1.2 + 1 2.3 + ... + 1 9.10 = 9 10 < 1.

b ) 3 2.5 + 3 5.8 + 3 8.11 + 3 11.14 + 3 14.17 + 3 17.20 = 1 2 − 1 20 < 1 2 .

c ) T a   c ó     1 2 2   < 1 1.2 ; 1 3 2 < 1 2.3 ; 1 4 2 < 1 3.4 ; ... ; 1 25 2 < 1 24.25 .

D o   đ ó , 1 2 2   + 1 3 2 + 1 4 2 + 1 25 2 < 1 1.2 + 1 2.3 + 1 3.4 + ... + 1 24.25 < 1.