\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\)\(\frac{1}{132}\)= \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{11\cdot12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{11}-\frac{1}{12}\)\(=1-\frac{1}{12}=\frac{11}{12}\)
B = 5/1.4 + 5/4.7 + 5/7.10 + ... + 5/97.100
B = 5/3.(3/1.4 + 3/4.7 + 3/7.10 + ... + 3/97.100)
B = 5/3.(1 - 1/4 +1/4 -1/7 +1/7 - 1/10 + ... + 1/97 - 1/100)
B = 5/3.(1 - 1/100)
B = 5/3.99/100
B = 33/20
B = 5/1.4 + 5/4.7 + 5/7.10 + ... + 5/97.100
B = 5/3.(3/1.4 + 3/4.7 + 3/7.10 + ... + 3/97.100)
B = 5/3.(1 - 1/4 +1/4 -1/7 +1/7 - 1/10 + ... + 1/97 - 1/100)
B = 5/3.(1 - 1/100)
B = 5/3.99/100
B = 33/20