Giúp mình

Ta có: \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{2004.2005.2006}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{2004.2005}-\frac{1}{2005.2006}\)

\(=\frac{1}{1.2}-\frac{1}{2005.2006}\)

\(=\frac{1}{2}-\frac{1}{4022030}\)

\(=-40220295.\)

\(=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{2}-\frac{1}{3}-\frac{1}{4}+...-\frac{1}{2005}+\frac{1}{2004}-\frac{1}{2005}-\frac{1}{2006}\)

\(=1-\frac{1}{2006}=\frac{2005}{2006}\)

3299/9900 nho k cho minh nha

A= 1/1.2.3+1/2.3.4+.....+1/98.99.100

2A = 2/1.2.3+ 2/2.3.4+....+2/98.99.100

Ta có: 2/1.2.3 = 1/1.2 - 1/2.3

Tương tự: 2/2.3.4 = 1/2.3 - 1/3.4

...........2/98.99.100 = 1/98.99 - 1/99.100

2A = 1/1.2 - 1/99.100 = 4949/9900

Vậy A = 4949/9900 : 2 = 4949/19800

Tích nha?

1/1.2.3 + 1/2.3.4 +....+1/98.99.100

= 1/2 . (3-1/1.2.3 + 4-2/2.3.4 +....+ 100-98/98.99.100)

= 1/2 . (3/1.2.3 -1/1.2.3 + 4/2.3.4 - 2/2.3.4 +.......+ 100/98.99.100 - 98/98.99.100)

= 1/2 . (1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 +......+ 1/98.99 - 1/99.100)

= 1/2 . (1/2 - 1/9900)

= 1/2 . 4949/9900

= 4949/19800

A=11.2.3+12.3.4+13.4.5+...+198.99.100=11.2−12.3+12.3−13.4+...+198.99−199.100=11.2−199.100=494919800

nhân tổng trên cho 2 ta có;

2/1.2.3+2/2.3.4+.........+2/98.99.100

=1/1.2-1/2.3+1/2.3-1/3.4+........+1/98.99-1/99.100

=1/1.2-1/99.100

=4949/9900

/

=1/1.2.3+1/2.3.4+1/3.4.5+............+1/98.99.100

 $=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)$

$=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9900}\right)$

$=\frac{1}{2}\cdot \frac{4949}{9900}$

$=\frac{4949}{19800}$

cho mình xin lỗi vì đáp án mình gửi lên nó bị lỗi nhá