B = \(\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}\)

\(=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+199\)

\(=\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+...+\left(\frac{198}{2}+1\right)+1\)

(từ 1 đến 198 có 198 số hạng nên còn 1 số 1)

\(=\frac{200}{199}+\frac{200}{198}+...\frac{200}{2}+\frac{200}{200}\)

\(=200\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{\text{4}}+...+\frac{1}{200}\right)=200A\)

=> B = 200A => \(\frac{A}{B}=\frac{1}{200}\)

Vậy \(\frac{A}{B}=\frac{1}{200}\)

B= \(\frac{1}{199}\) + \(\frac{2}{198}\) + ... + \(\frac{198}{2}\) + \(\frac{199}{1}\)

B= ( \(\frac{1}{199}\) + 1) + ( \(\frac{2}{198}\) +1) +...+ ( \(\frac{198}{2}\) +1) +1 ( Mình tách 199 ra thành 199 số hạng rồi cộng thêm vào mỗi phân số)

B= \(\frac{200}{199}\) + \(\frac{200}{198}\) + \(\frac{200}{197}\) +...+\(\frac{200}{2}\)

B= 200( \(\frac{1}{199}\) + \(\frac{1}{198}\) +...+ \(\frac{1}{2}\) ) 

B= 200 ( \(\frac{1}{2}\) + \(\frac{1}{3}\) +...+ \(\frac{1}{198}\) + \(\frac{1}{199}\) ) = 200 A

Ta thấy A=1A, B=200A Suy ra \(\frac{A}{B}\) = \(\frac{1}{200}\)

Giúp mình đi. Mai phải nộp bài rồi 

uk đợi mk xíu, bài này dài lắm

\(B=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}\)

\(=\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+\left(\frac{3}{197}+1\right)+...+\left(199-1-1-1-...1\right)\)(198 chữ số 1)

\(=\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+1=200.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{197}+\frac{1}{198}+\frac{1}{199}+\frac{1}{200}\right)=200.A\)

\(\Rightarrow\frac{A}{B}=\frac{A}{200.A}=\frac{1}{200}\)

i don't now

mong thông cảm !

...........................

\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}}\)

\(=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+\left(\frac{3}{197}+1\right)+...+\left(\frac{198}{2}+1\right)+1}\)

\(=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}+\frac{200}{200}}\)

\(=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{200\cdot\left(\frac{1}{200}+\frac{1}{199}+\frac{1}{198}+\frac{1}{197}+...+\frac{1}{2}\right)}\)

\(=\frac{1}{200}\)

\(D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{198}+\frac{1}{199}}{\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}}\)

\(D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{198}+\frac{1}{199}}{\left[\frac{1}{199}+1\right]+\left[\frac{2}{198}+1\right]+\left[\frac{3}{197}+1\right]+...+\left[\frac{198}{2}+1\right]}\)

\(D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{198}+\frac{1}{199}}{\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}}\)

\(D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{198}+\frac{1}{199}}{200\left[\frac{1}{199}+\frac{1}{198}+\frac{1}{197}+...+\frac{1}{2}\right]}=\frac{1}{200}\)

S= 1/199 + 2/198 + ... + 198/2 + 199/1

S= (1/199 + 1) + (2/198 + 1)+ ... + (198/2  + 1) +1

S= 200/200 + 200/199 + 200/198 + ... + 200/2 

S= 200.(1/200 + 1/199 + ... + 1/2)

Suy ra , B=(1/2 + 1/3 + ... +1/200) : 200.(1/2 + 1/3 + ... + 1/200)

B=1 : 200 = 1/200

Đặt: \(\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{199}{1}\)là B

Cộng 1 vào mỗi phần số trừ phân số cuối cùng ta sẽ được:

B= \(\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+...+\left(\frac{198}{2}+1\right)+1\)

=> B= \(\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}+1\)

=> B= \(\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}+\frac{200}{200}\)

=> B= \(200\left(\frac{1}{200}+\frac{1}{199}+\frac{1}{198}+...+\frac{1}{2}\right)\)

Đặt \(A=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200}\) => B= \(200\) X A

=> \(\frac{A}{B}\)\(=\frac{1}{200}\)

=> \(\left(x-20\right).\frac{1}{200}=\frac{1}{2000}\)

=>\(x-20\) =\(\frac{1}{2000}:\frac{1}{200}\)

=> \(x-20=\).......................... Bạn tự làm tiếp nhé, chúc bạn học tốt !!!^^\(\)

Câu3: Ký hiệu [a,b] và (a,b) là gì ? Bạn.

Câu 1:

\(B=\frac{1}{199}+1+\frac{2}{198}+1+\frac{3}{197}+1+...+\frac{198}{2}+1+\frac{199}{1}+1-199\)

\(=\frac{200}{199}+\frac{200}{198}+\frac{200}{197}+...+\frac{200}{2}+1=\frac{200}{200}+\frac{200}{199}+\frac{200}{198}+...+\frac{200}{2}\)

\(=200\cdot\left(\frac{1}{200}+\frac{1}{199}+\frac{1}{198}+...+\frac{1}{2}\right)=200\cdot A\)

Vậy, \(\frac{A}{B}=\frac{1}{200}\).

Mình nghĩ  [a, b] là BCNN, còn (a, b) là ƯCLN