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5 tháng 7 2017

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

= 1/2 - 1/9900

= 4949/9900

k cho minh nha

chuc ban hoc tot

5 tháng 7 2017

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

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

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

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

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

\(=2.\left[\frac{1}{2}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\right]\)

\(=2.\left[\frac{1}{2}.\left(1-\frac{1}{100}\right)\right]\)

\(=2.\left(\frac{1}{2}.\frac{99}{100}\right)\)

\(=\left(2.\frac{1}{2}\right).\frac{99}{100}\)

\(=1.\frac{99}{100}\)

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

A=1/2 *(1/1*2-1/2*3+1/2*3-1/3*4+........+1/98*99-1/99*100)

=1/2*(1/2-1/99*100)

=1/2*(4950-1/9900)

=4950/19800

14 tháng 4 2019

\(A=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{98\cdot99\cdot100}\)

\(A=\frac{1}{2}\left[\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{98\cdot99\cdot100}\right]\)

\(A=\frac{1}{2}\left[\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+....+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\right]\)

\(A=\frac{1}{2}\left[\frac{1}{2}-\frac{1}{99\cdot100}\right]=\frac{1}{2}\cdot\frac{4949}{9900}=\frac{4949}{19800}\)

8 tháng 11 2016

A = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{99.100.101}\)

=> A = \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}-\frac{1}{100.101}\right)\)

= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{100.101}\right)\)

= \(\frac{1}{2}.\frac{5049}{10100}\)

= \(\frac{5049}{20200}\)

8 tháng 11 2016

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{99.100.101}\)

\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{99.100.101}\)

Ta thấy:

\(\frac{2}{1.2.3}=\frac{1}{1.2}-\frac{1}{2.3};\frac{2}{2.3.4}=\frac{1}{2.3}-\frac{1}{3.4};...;\frac{2}{99.100.101}=\frac{1}{99.100}-\frac{1}{100.101}\)

\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}-\frac{1}{100.101}\)

\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{100.101}\)

\(\Rightarrow2A=\frac{1}{2}-\frac{1}{10100}\)

\(\Rightarrow2A=\frac{5050}{10100}-\frac{1}{10100}\)

\(\Rightarrow2A=\frac{5049}{10100}\Rightarrow A=\frac{5049}{10100}:2=\frac{5049}{20200}\)

 

11 tháng 8 2016

Ta có

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

2Z =  2/1.2.3 + 2/2.3.4 + 2/3.4.5 + ... + 2/98.99.100

2Z = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 + ... + 1/98.99 - 1/99.100

2Z = 1/1.2 - 1/99.100

2Z = 4949/9900

=> Z = 4949/19800

=> 4949/19800 . x = 49/200

                           x = 49/200 : 4949/19800

                           x = 99/101

Vậy x = 99/101

Ủng hộ nha

2 tháng 10 2020

a) \(A=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+...+\frac{2}{98\cdot99\cdot100}\)

\(A=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\)

\(A=\frac{1}{2}-\frac{1}{99\cdot100}=\frac{1}{2}-\frac{1}{9900}=\frac{4949}{9900}\)

b) \(B=\frac{17}{1\cdot3\cdot5}+\frac{17}{3\cdot5\cdot7}+\frac{17}{5\cdot7\cdot9}+...+\frac{17}{47\cdot49\cdot51}\)

\(B=\frac{17}{4}\left(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+...+\frac{4}{47\cdot49\cdot51}\right)\)

\(B=\frac{17}{4}\left(\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5\cdot7}+...+\frac{1}{47\cdot49}-\frac{1}{49\cdot51}\right)\)

\(B=\frac{17}{4}\left(\frac{1}{3}-\frac{1}{2499}\right)=\frac{17}{4}\cdot\frac{832}{2499}=\frac{208}{147}\)

21 tháng 3 2015

T/c:A=1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+...+1/97*98*99+1/98*99*100

2A=2/1*2*3+2/2*3*4+2/3*4*5+2/4*5*6+...+2/97*98*99+1/98*99*100

2A=(1/1*2-1/2*3)+(1/2*3-1/3*4)+(1/3*4-1/4*5)+.....+(1/97*98-1/98*99)+(1/98*99-1/99*100)

2A=1/2+1/99*100

A=tự tính nha

19 tháng 2 2018

A= [(1/2-1/2*3)/2]+[(1/2-1/3*4)/2]+...+[(1/2-1/99*100)/2]

A=(1/2-1/99*100)/2

A=-101/198/2

A=-101/396