a. \(\dfrac{1}{2.4}\) + \(\dfrac{1}{4.6}\) + \(\dfrac{1}{6.8}\) + ...... + \(\dfrac{1}{20.22}\)

= 1/2 ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ..... + 1/20 - 1/22)

=1/2 ( 1/2 - 1/22)

= 1/2 . 5/11

= 5/22

b. 1+ 2/3 + 2/6 + 2/10 +...+ 2/45

=>1/2.(1+2/3+2/6+....+2/45)=1/2+2/6+2/12+...+2/90

=1/2+2/2.3+2/3.4+...+2/9.10
=2.(1/4+3-2/2.3+4-3/3.4+...+10-9/9.10)

=2. ( 1/4+1/2-1/3+1/3-1/4+.....+1/9-1/10)
= 2.( 1/4-1/10)=2.3/20=3/10

=> vì 1/2.*=3/10

=> *=3/10:1/2=3/5

tick mình nhé

B = 1 + \(\dfrac{2}{3}\) + \(\dfrac{2}{6}\) +\(\dfrac{2}{10}\) + \(\dfrac{2}{15}\)+...+ \(\dfrac{2}{45}\)

B = 1 + 2.(\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\)+...+ \(\dfrac{1}{45}\))

B = 1 + \(\dfrac{4}{2}\).(\(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) +\(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + ...+ \(\dfrac{1}{45}\))

B = 1 + 4.( \(\dfrac{1}{6}\) +\(\dfrac{1}{12}\)+ \(\dfrac{1}{20}\)+ \(\dfrac{1}{30}\)+...+ \(\dfrac{1}{90}\))

B = 1 + 4.(\(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\)+ \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\)+...+\(\dfrac{1}{9.10}\))

B = 1 + 4 .( \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\)+...+ \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\))

B = 1 + 4.( \(\dfrac{1}{2}\) - \(\dfrac{1}{10}\))

B = 1 + 4. \(\dfrac{2}{5}\)

B = \(\dfrac{13}{5}\)

A = \(\dfrac{1}{2.4}\) + \(\dfrac{1}{4.6}\) + \(\dfrac{1}{6.8}\) +...+ \(\dfrac{1}{20.22}\)

A = \(\dfrac{2}{2}\).( \(\dfrac{1}{2.4}\) + \(\dfrac{1}{4.6}\) + \(\dfrac{1}{6.8}\)+...+ \(\dfrac{1}{20.22}\))

A = \(\dfrac{1}{2}\).( \(\dfrac{2}{2.4}\) + \(\dfrac{2}{4.6}\) + \(\dfrac{2}{6.8}\)+...+ \(\dfrac{1}{20.22}\))

A = \(\dfrac{1}{2}\).( \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{8}\) +...+ \(\dfrac{1}{20}\) - \(\dfrac{1}{22}\))

A = \(\dfrac{1}{2}\).( \(\dfrac{1}{2}\) - \(\dfrac{1}{22}\))

A = \(\dfrac{1}{2}\) . \(\dfrac{5}{11}\)

A = \(\dfrac{5}{22}\) 

\(S=\dfrac{1}{1.3}-\dfrac{1}{2.4}+\dfrac{1}{3.5}-\dfrac{1}{4.6}+\dfrac{1}{5.7}-\dfrac{1}{6.8}+\dfrac{1}{7.9}-\dfrac{1}{8.10}\)

\(S=\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}\right)-\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+\dfrac{1}{8.10}\right)\)\(S=\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}\right)-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}\right)\)\(S=\left(1-\dfrac{1}{9}\right)-\left(1-\dfrac{1}{10}\right)\)

\(S=\dfrac{8}{9}-\dfrac{9}{10}=\dfrac{-1}{10}\)

a) \(A=2.4+4.6+...+98.100\)

\(\Rightarrow6A=2.4.6+4.6.6+....+98.100.6\)

\(=2.4.6+4.6.\left(8-2\right)+...+98.100.\left(102-96\right)\)

\(=2.4.6+4.6.8-2.4.6+...+98.100.102-98.98.100\)

\(=98.100.102\)

\(=999600\)

\(\Rightarrow A=\frac{999600}{6}=166600\)

PHẦN khác tương tự mẹo là xem tích đầu tiên rồi nhân cả biểu thức đó với số liền sau của tích các số đầu nhưng mà có quy luật

a)
\(\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10}{3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20}\)

\(=\frac{1\cdot2\cdot\left(1+2\cdot2+3\cdot3+4\cdot4+5\cdot5\right)}{3\cdot4\cdot\left(1+2\cdot2+3\cdot3+4\cdot4+5\cdot5\right)}\)

\(=\frac{1\cdot2}{3\cdot4}=\frac{1}{6}\)

b) \(\frac{12\cdot13+24\cdot26+36\cdot39}{24\cdot26+48\cdot52+72\cdot78}\)

\(=\frac{12\cdot13\cdot\left(1+2\cdot2+3\cdot3\right)}{24\cdot26\cdot\left(1+2\cdot2+3\cdot3\right)}\)

\(=\frac{12\cdot13}{24\cdot26}=\frac{1}{4}\)

\(\frac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}=\frac{2\cdot3\cdot\left(1+2\cdot2+7\cdot7\right)}{3\cdot5\cdot\left(1+2\cdot2+7\cdot7\right)}=\frac{2\cdot3}{3\cdot5}=\frac{2}{5}\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=\dfrac{1}{2}\cdot\dfrac{4}{10}=\dfrac{2}{10}=\dfrac{1}{5}\)

\(\dfrac{1}{2.4}hay\dfrac{1}{2}.4\)

S= 1/2.4+1/4.6+1/6.8+1/8.10

S= 1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10

S= 1/2-1/10

S= 2/5

Sai thì bình luận ch mình biết nha

\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}\)

\(S=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\)

\(S=\frac{1}{2}-\frac{1}{10}\)

\(S=\frac{2}{5}\)

S = 1 / 2.4 + 1/ 4.6 + 1 / 6.8 + 1 / 8.10

2S = 2 / 2.4 + 2 / 4.6 + 2/ 6.8 + 2 / 8.10

2S = 1 2 - 1 / 4 + 1 / 4 - 1 / 6 + 1 / 6 - 1 / 8 + 1 / 8 - 1 / 10

2S = 1 / 2 - 1 / 10

2S = 2 / 5 

  S = 2 / 5 : 2

  S = 1 / 5 

\(\frac{1}{2.4}+\frac{1}{4.6}+....+\frac{1}{2016.2018}\)

\(=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2016.2018}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2018}\right)=\frac{1}{2}.\frac{504}{1009}=\frac{252}{1009}\)

mơn bn nha

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2016.2018}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(=\frac{1}{2}+\left(-\frac{1}{4}+\frac{1}{4}\right)+\left(-\frac{1}{6}+\frac{1}{6}\right)+...+\left(-\frac{1}{2016}+\frac{1}{2016}\right)-\frac{1}{2018}\)

\(=\frac{1}{2}+0+0+0+...+0-\frac{1}{2018}\)

\(=\frac{1}{2}-\frac{1}{2018}\)

\(=\frac{1009}{2018}-\frac{1}{2018}\)

\(=\frac{1008}{2018}=\frac{504}{1009}\)

Ai thấy tớ đúng k nha