Ta có: B=1/2 ² +1/3 ² +1/4 ²+ 1/5 ² +1/6 ² +1/7 ² +1/8 ²
Xét 1/2² = 1/2.2 < 1/1.2 = 1-1/2
1/3² = 1/3.3 < 1/2.3 =1/2 -1/3
1/4² =1/4.4 <1/3.4 = 1/3-1/4
....
1/8² =1/8.8 < 1/7.8 = 1/7-1/8
⇒ B=1/2 ² +1/3 ² +1/4 ²+ 1/5 ² +1/6 ² +1/7 ² +1/8 ² < 1-1/2+1/2-1/3+1/3-1/4...+1/7-1/8
⇒B < 1 - 1/8 = 7/8 <1
=> B <1 (đpcm)
Chúc bn học tốt !