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16 tháng 2 2015

\(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)=\frac{4949}{19800}\)

13 tháng 10 2016

\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\)

\(2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{100-98}{98.99.100}\)

\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

\(2A=\frac{1}{2}-\frac{1}{99.100}=\frac{49}{99.100}\Rightarrow A=\frac{49}{2.99.100}\)

23 tháng 4 2018

\(A=2.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\right)\)

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

\(A=2.\left(\frac{1}{1.2}-\frac{1}{99.100}\right)\)

\(A=2\cdot\frac{4949}{9900}=\frac{4949}{4950}\)

10 tháng 8 2016

\(2S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(2S=\frac{1}{2}-\frac{1}{9900}\)

\(2S=\frac{4949}{9900}\)

\(S=\frac{4949}{19800}\)

11 tháng 8 2016

Ta xét : \(\frac{1}{1.2}-\frac{1}{2.3}=\frac{2}{1.2.3}\)

\(\frac{1}{2.3}-\frac{1}{3.4}=\frac{2}{2.3.4}\)

...

\(\frac{1}{98.99}-\frac{1}{99.100}=\frac{2}{98.99.100}\)

Ta có : 2S = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

=> 2S = \(\frac{1}{1.2}-\frac{1}{99.100}\)

=> 2S = \(\frac{4949}{9900}\)

=> S = \(\frac{4949}{19800}\)

30 tháng 7 2015

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

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

2A=1/1.2-1/99.100

2A=1/2-1/9900

2A=4949/9900

A=4949/19800

5 tháng 4 2018

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

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

2A=1/1.2-1/99.100

2A=1/2-1/9900

2A=4949/9900

A=4949/19800

8 tháng 9 2017

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

\(=\frac{1}{2}-\frac{1}{9900}=\frac{4950}{9900}-\frac{1}{9900}=\frac{4949}{9900}\)

8 tháng 9 2017

Ta có:

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)

\(\Rightarrow\frac{1}{2}A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+....+\frac{2}{98.99.100}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+....+\frac{1}{98.99}-\frac{1}{99.100}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{1.2}-\frac{1}{99.100}\)

\(\Rightarrow A=\frac{4949}{9900}.\frac{1}{2}=\frac{4949}{19800}\)

6 tháng 7 2016

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{4.5.6}+....+\frac{1}{98.99.100}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{100}\)

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

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

6 tháng 7 2016

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

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

\(=\frac{1}{2}.\frac{4949}{9900}\)

\(=\frac{1}{19800}\)

11 tháng 4 2019

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)

\(=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{99.100}\right)\)

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

\(=\frac{1}{2}.\frac{4949}{9900}\)

\(=\frac{4949}{19800}\)

30 tháng 1 2016

Kết bạn vs mk nha !!!