Question

[hieu pro lb]

1/2*3+1/3*4+...+1/99*100

3/1*4+3/4*7+...3/91*94

bạn nào làm chi tiết ra nhé!!!!!!!!!!

thank you :p

Answer 1

[Võ Đông Anh Tuấn]

a) \(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{99\times100}\)

    \(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

      \(=1-\frac{1}{100}\)

          \(=\frac{99}{100}\)

b) \(\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{3}{91\times94}\)

 \(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{91}-\frac{1}{94}\)

   \(=\frac{1}{1}-\frac{1}{94}\)

    \(=\frac{93}{94}\)

Answer 2

[SKT_Rengar Thợ Săn Bóng Đêm]

1/2x3 + 1/3x4 + ..... + 1/99x100

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

= 1/2 - 1/100

= 49/100

3/1x4 + 3/4x7 + .... + 3/91x94

= 3 - 3/4 + 3/4 - 3/7 + .....+ 3/91 - 3/94

= 3 - 3/94

= 279/94