làm ơn tách ra giùm mk

ta có  \(2004+\frac{2003}{2}+\frac{2002}{3}+...+\frac{1}{2004}\)

         \(=\left(1+\frac{2003}{2}\right)+\left(1+\frac{2002}{3}\right)...\left(1+\frac{1}{2004}\right)+1\)

         \(=\frac{2005}{2}+\frac{2005}{3}+...+\frac{2005}{2004}+\frac{2005}{2005}\)

         \(=2005\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2004}+\frac{1}{2005}\right)\)

          \(\Rightarrow\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2005}}{\frac{2004}{1}+\frac{2003}{2}+\frac{2002}{3}+...+\frac{1}{2004}}\)

         \(=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2004}+\frac{1}{2005}}{2005\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2004}+\frac{1}{2005}\right)}\)

         \(=\frac{1}{2005}\)

\(B=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times...\times\left(1-\frac{1}{2004}\right)\)

\(=\left(\frac{2}{2}-\frac{1}{2}\right)\times\left(\frac{3}{3}-\frac{1}{3}\right)\times...\times\left(\frac{2003}{2003}-\frac{1}{2003}\right)\times\left(\frac{2004}{2004}-\frac{1}{2004}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times...\times\frac{2002}{2003}\times\frac{2003}{2004}\)

\(=\frac{1\times2\times...\times2002\times2003}{2\times3\times...\times2003\times2004}\)

\(=\frac{1}{2004}\)

=> B = 1/2 * 2/3 * 3/4 * 4/5 *...* 2002/2003 * 2003/2004                                                                                                                             = 1/2004

\(B=\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x...x\left(1-\frac{1}{2-2003}\right)x\left(1-\frac{1}{2004}\right)\)

\(B=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{2002}{2003}x\frac{2003}{2004}\)

\(B=\frac{1}{2004}\)

B = ( 1 - 1/2 ) . ( 1 - 1/3 ) . ( 1 - 1/4 ) - ( 1 - 1/5 )...... . ( 1 - 1/2003 ) . ( 1 - 1/2004 )

= 1/2 . 2/3 . 3/4 . 4/5 ....... . 2002/2003 . 2003/2004

= 1/2004

HỌC TỐT!

Đặt B = 2004+2003/2+2002/3+...+1/2004 B có 2004 phân số tách số 2004 = 1+1+1+...+1(2004 số 1) ghép 2004 số 1 vào từng nhóm như sau: B=(1+ 2003/2)+ (1+ 2002/3)+...+(1+1/2004) +1 B = 2005/2+2005/3+......+2005/2004+2005/2005 B = 2005x(1/2+1/3+....+1/2004+1/2005) Vậy A = 2005

Đặt B = 2004+2003/2+2002/3+...+1/2004
B có 2004 phân số
tách số 2004 = 1+1+1+...+1(2004 số 1)
ghép 2004 số 1 vào từng nhóm như sau:
B=(1+ 2003/2)+ (1+ 2002/3)+...+(1+1/2004) +1
B = 2005/2+2005/3+......+2005/2004+2005/2005 
B = 2005x(1/2+1/3+....+1/2004+1/2005)
Vậy A = 2005

nguyên một hàng mk đọc ko hỉu????????????

không hiểu......>><

khó hiểu quá

ko bit

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