Bài này khi sáng mình mới học 100% là đúng luôn.

1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + ........... + 1/99x100.

=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+..........1/98-1/99+1/99-1/100.

=1/1-1/100=99/100.

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)

1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + ........... + 1/99x100.

=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+..........1/98-1/99+1/99-1/100.

=1/1-1/100

=99/100

21320 đúng ko

gợi ý có 5 chữ số

nhanh lên

1/1x2+1/2x3+1/3x4+.........1/999x1000+1

=1/1-1/1000+1

=1999/1000

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{5x7}\)

Đề sai hay bạn sai v ạ, tính nhanh thì lẽ ra phải là 6x7

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{5.6}+\dfrac{1}{5.7}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{5}-\dfrac{1}{7}\)

\(=1-\dfrac{1}{6}+\dfrac{1}{5}-\dfrac{1}{7}=\dfrac{187}{210}\)

ko nhaa cô giáo mik viết thế mà ko sai đou

=1999/1000

Mik chắc chắn vì mik thi Violympic r

ra 1999/1000 nha bạn

\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.........+\frac{1}{999x1000}+1\)

= \(1-\frac{1}{1000}+1\)

= \(\frac{999}{1000}+1\)

= \(\frac{1999}{1000}\)

A = \(\frac{1}{1}\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{4}\)

A = 1 - \(\frac{1}{4}\)

A = \(\frac{3}{4}\)

A = 2 + 3/2 + 4/3

A = 2/1 + 3/2 + 4/3 

A = 12 / 6 + 9 / 6 + 8 / 6

A = 12/6 + ( 9/6 + 8/6 )

A = 12/6 + 17/6

A = 29/6

A = 1/2 + 1/6 + 1/12 

A = 6/12 + 2/12 + 1/12 

A =  9/12

A = 3/4

~ Hok ~

Bài 1:

Đặt \(A=\frac{2}{1x2}+\frac{2}{2x3}+\frac{2}{3x4}+...+\frac{2}{18x19}+\frac{2}{19x20}\)

\(\frac{A}{2}=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{18x19}+\frac{1}{19x20}\)

\(\frac{A}{2}=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{19-18}{18x19}+\frac{20-19}{19x20}\)

\(\frac{A}{2}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}=1-\frac{1}{20}=\frac{19}{20}\)

\(A=\frac{2x19}{20}=\frac{19}{10}\)

Bài 2:

Đặt \(B=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{8x9}+\frac{1}{9x10}\)

Làm tương tự câu 1 có \(B=1-\frac{1}{10}=\frac{9}{10}\)

\(Bx100=\frac{9}{10}x100=90\)

=> \(\left[\frac{5}{2}:\left(x+\frac{206}{100}\right)\right]:\frac{1}{2}=1\)

=> \(\left[\frac{5}{2}:\left(x+\frac{206}{100}\right)\right]=\frac{1}{2}\)

=>  \(x+\frac{206}{100}=\frac{5}{2}:\frac{1}{2}=5\Rightarrow x=5-\frac{206}{100}=\frac{294}{100}=\frac{147}{50}\)

bài 1 đáp án là:19/10

2:147/50

đáp án bài 1 là: 19/10

đáp án bài 2 là 147/50

\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+....+\dfrac{1}{24\times25}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{24}-\dfrac{1}{25}\)

\(=1-\dfrac{1}{25}\)

\(=\dfrac{24}{25}\)

Nhanh giúp mình với cả nhà ơi