Question

Giup mình cái nè:

Tính: 

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

Answer 1

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

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

= 1 - 1/100

= 99/100

Answer 2

99/100

Answer 3

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

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

= 1 - 1/100

= 99/100

Answer 4

1/1x2 + 1/2x3 + 1/3x4 + ... + 1/99x100

Đặt A = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/99x100

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

A = 1/1 - 1/100

A = 99/100

 Vậy A = 99/100

Answer 5

Cảm ơn các bạn nha

Answer 6

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

\(=\frac{2-1}{1\cdot2}+\frac{3-2}{2\cdot3}+\frac{4-3}{3\cdot4}+...+\frac{100-99}{99\cdot100}\)

\(=\frac{2}{1\cdot2}-\frac{1}{1\cdot2}+\frac{3}{2\cdot3}-\frac{2}{2\cdot3}+\frac{4}{3\cdot4}-\frac{3}{3\cdot4}+...+\frac{100}{99\cdot100}-\frac{99}{99\cdot100}\)

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

\(=1-\frac{1}{100}=\frac{99}{100}\)

Answer 7

1/1 x 2 + 1/2 x 3 + 1/3 x 4 + ...+ 1/99 x100 = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/ 99 x 100

                                                               =  1 - 1/100

                                                               = 99/100.

       k mk nha !