Ta có: \(A=\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+\cdots+\frac{1}{99\cdot100}\)

\(=1-\frac12+\frac13-\frac14+\cdots+\frac{1}{99}-\frac{1}{100}\)

\(=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{99}+\frac{1}{100}-2\left(\frac12+\frac14+\cdots+\frac{1}{100}\right)\)

\(=1+\frac12+\frac13+\frac14+\cdots+\frac{1}{99}+\frac{1}{100}-1-\frac12-\cdots-\frac{1}{50}\)

\(=\frac{1}{51}+\frac{1}{52}+\cdots+\frac{1}{100}\)

=>\(A-B=-\frac{1}{50}\)

xét B ta có:

B=1/1.2+1/3.4+1/5.6+...+1/99.100

B=1-1/2+1/3-1/4+1/5-1/6+...+1/99-100

B=(1+1/3+1/5+...+1/99)-(1/2+1/4+...+1/100)

B=(1+1/3+1/5+...+1/99)+(1/2+1/4+1/6+...+1/100)-2(1/2+1/4+1/6+...+1/100)

B=(1+1/2+1/3+...+1/99+1/100)-(1+1/2+1/3+1/4+...+1/50)

=>B=1/51+1/52+1/53+...+1/100

=>A/B=1/51+1/52+...+1/100:1/51+1/52+...+1/100=1 (đpcm)

Đó là cách nhanh nhất để giải nếu bn ko hỉu thì mik sẽ giải chi tiết cho

chúc bn học tốt ^-^

mik nhớ kq là ..........50 thì phải

B=1/1.2+1/3.4+1/5.6+...+1/99.100

=1-1/2+1/3-1/4+1/5-1/6+...+1/99-1/100

=(1+1/3+1/5+...+1/99)-(1/2+1/4+1/6+...+1/100)

=(1+1/2+1/3+1/4+1/5+1/6+...+1/99+1/100)-2(1/2+1/4+1/6+...+1/100)

=(1+1/2+1/3+1/4+...+1/100)-(1+1/2+1/3+..+1/50)

=1/51+1/52+1/53+..+1/100 (1)

A=1/51+1/52+1/53+..+1/100 (2)

(1),(2)=> A/B=1

\(\frac{A}{B}=1\)

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