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
