45854

212122512122

1

1

1

1123

4564

454

3546434

mình không biết mà có biết cũng không có hứng trả lời

ai nhanh nhat minh k cho dung thi cung k[lam loi giai ra nha]

cái này chắc đề sai

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 ^-^

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

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

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

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

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

b: Ta có: \(\frac{1}{51}<\frac{1}{50};\frac{1}{52}<\frac{1}{50};\ldots;\frac{1}{75}<\frac{1}{50}\)

Do đó: \(\frac{1}{51}+\frac{1}{52}+\cdots+\frac{1}{75}<\frac{1}{50}+\frac{1}{50}+\cdots+\frac{1}{50}=\frac{25}{50}=\frac12\) (1)

TA có: \(\frac{1}{76}<\frac{1}{75};\frac{1}{77}<\frac{1}{75};\ldots;\frac{1}{100}<\frac{1}{75}\)

Do đó: \(\frac{1}{76}+\frac{1}{77}+\ldots+\frac{1}{100}<\frac{1}{75}+\frac{1}{75}+\cdots+\frac{1}{75}=\frac{25}{75}=\frac13\) (2)

Từ (1),(2) suy ra \(\left(\frac{1}{51}+\frac{1}{52}+\cdots+\frac{1}{75}\right)+\left(\frac{1}{76}+\frac{1}{77}+\cdots+\frac{1}{100}\right)<\frac12+\frac13\)

=>\(A<\frac56\) (3)

Ta có: \(\frac{1}{51}>\frac{1}{75};\frac{1}{52}>\frac{1}{75};\ldots;\frac{1}{75}=\frac{1}{75}\)

Do đó: \(\frac{1}{51}+\frac{1}{52}+\cdots+\frac{1}{75}>\frac{1}{75}+\frac{1}{75}+\cdots+\frac{1}{75}=\frac{25}{75}=\frac13\) (4)

Ta có: \(\frac{1}{76}>\frac{1}{100};\frac{1}{77}>\frac{1}{100};\ldots;\frac{1}{100}=\frac{1}{100}\)

Do đó: \(\frac{1}{76}+\frac{1}{77}+\cdots+\frac{1}{100}>\frac{1}{100}+\frac{1}{100}+\cdots+\frac{1}{100}=\frac{25}{100}=\frac14\) (5)

Từ (4),(5) suy ra \(\left(\frac{1}{51}+\frac{1}{52}+\cdots+\frac{1}{75}\right)+\left(\frac{1}{76}+\frac{1}{77}+\cdots+\frac{1}{100}\right)>\frac13+\frac14\)

=>A>7/12(6)

Từ (3),(6) suy ra 5/6<A<7/12