Question

1.tính

B= 12/ 1.4.7 + 12/ 4.7.10 + 12/ 7.10.13 +....+ 12/54.57.60

2.chứng minh

a)  A= 1+ 1/2^2 + 1/3^2 +...+1/100^2 < 2

b) B= 1/5 + 1/13 +1/25 +...+1/n^2+(n+1)^2< 1/2

Answer 1

1

B= 12/1.4.7 + 12/4.7.10 + 12/7.10.13 + ... + 12/54.57.60

=> 1/2B= 6/1.4.7 + 6/4.7.10 + 6/7.10.13 + ... + 6/54.57.60

=> 1/2B = 1/1.4 - 1/4.7 +1/4.7 - 1/7.10 +1/7.10 - 1/10.13 + ... + 1/54.57 - 1/57.60

=> 1/2B =1/1.4 - 1/57.60

=> 1/2B = 1/4 - 1/3420

=> 1/2B = 427/1710

=> B = 427/1710 . 2

=> B = 427/855

Answer 2

2

A= 1+ 1/2² + 1/3² +...+1/100²

  =1+ 1/2.2 + 1/3.3 +...+ 1/100.100

=> A< 1+ 1/1.2 + 1/2.3 +...+ 1/99.100

   = 1+ 1 - 1/2 +1/2 - 1/3 +...+1/99 - 1/100

   = 2- 1/100 < 2

Vậy A < 2