Đáp án:
2875/462
Giải thích các bước giải:
B= 25/1.2.3 + 25/2.3.4 + 25/3.4.5 +..........+ 25/20.21.22
=> B=25/2 . ( 25/1.2.3 + 25/2.3.4 + 25/3.4.5 + ...............+ 25/20.21.22)
=> B= 25/2.[1/2.(2/1.3)+1/3.(2/2.4)+1/4.(2/3.5)+...........+1/21.(2/20.22)]
=> B= 25/2.[1/2.(1−1/3)+1/3.(1/2−1/4)+1/4.(1/3−1/5)+...+1/21.(1/20−1/22)
=> B=25/2 .(1/1.2−1/2.3+1/2.3−1/3.4+1/3.4−1/4.5+...+1/20.21−1/21.22)
=>B=25/2.(1/1.2−1/21.22)
=>B=2875/462