a, Điều đương nhiên

b,\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{999.1000}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.........+\frac{1}{999}-\frac{1}{1000}\)

= \(1-\frac{1}{1000}\)

= \(\frac{999}{1000}\)

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{999.1000}+1\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{999}-\dfrac{1}{1000}+1\)

\(=1-\dfrac{1}{1000}+1\)

\(=\dfrac{1999}{1000}\).

dễ lắm nha

La 1,999 nha!

Là 1,999 mình học rồi

\(\frac{1999}{1000}\)

ủng hộ mk

1/1*2+1/2*3+,,,,,+1/999*1000+1

=1/1-1/2+1/2-1/3+,,,,+1/999-1/1000+1

=1-1/1000+1

=1+1-1/1000

=2-1/1000

=1999/1000

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}+1\)

Đặt \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{999.1000}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{999}-\frac{1}{1000}\)

\(\Rightarrow A=1-\frac{1}{1000}=\frac{999}{1000}\)

Thay vào ta có : \(\frac{999}{1000}+1=\frac{1999}{1000}\)

Vậy ...

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

= ( 1 / 1 x2 + 1/ 2 x3 + 1/ 3x4 + ....+ 1/999x 1000 ) + 1

= ( 1 x1 / 1 x2 + 1x2 / 2x3 + 1x 3 / 3x4 + ..... 1x 999 / 999x 1000 ) + 1

= ( 1 - 1 / 2 + 1 / 2 - 1 / 3 - 1 / 3 - 1 / 4 + ........+ 1 / 999 - 1 / 1000 )  + 1 

= ( 1 - 1 / 1000 ) + 1

= 999 / 1000 + 1

= 1999 / 1000

Tk tớ nha

ta thấy 1/1-1/2=1/1x2

vậy tích đó \(1-\frac{1}{2}+\frac{1}{2}.............-\frac{1}{1000}=1-\frac{1}{1000}=\frac{999}{1000}\)

1999/1000

1999/1000 tk nha mk nhanh ma

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{999\cdot1000}+1\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{999}-\frac{1}{1000}+1\)

\(=1-\frac{1}{1000}+1\)

\(=\frac{999}{1000}+1=\frac{1999}{1000}\)

1/1*2  + 1/2*3 + 1/3*4 +................+1/999*1000 +1

=1/2 + 1/6 + 1/12 + ....................+1/999000 +1 

=1-1/2 + 1/2-1/3 + 1/3-1/4 +...+ 1/999- 1/1000+1

=1- 1/1000+1

=999/1000+1

=1999/1000

1/1*2+1/2*3+1/3*4+1/4*5+...+1/999*1000+1

=1-1/1000+1

=1000+1-1/1000+1

=1000/1001

1999/1000 

tớ gặp bài này rối, k nhé