Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{2}{2004.2005}\)

Ta có: \(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{2004.2005}\)

\(A=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{2004.2005}\right)\)

\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{2004.2005}\right)\)

\(A=2.\left(\frac{1}{2}-\frac{1}{2005}\right)\)

\(A=\frac{2003}{2005}\)

bn ơi bn chưa nhân với 2

Con cuối cùng ko cần nhân vs 2 bởi tử là 2 rồi. Những con còn lại tử là 1 nên cả tử cả mẫu mới phải nhân vs 2.

Lm thế mới đặt đc 2 ra ngoài !

Chứ con cuối nhân 2 rồi thành \(\frac{2}{2004.2005}=\frac{4}{8036040}\)đặt 2 ra ngoài để lm gì hả ??

Đặt A = 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45

=> 1/2A = 1/4 + 1/6 + 1/12 + 1/20 + 1/30 + ... + 1/72 + 1/90

= 1/4 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/8.9 + 1/9.10

= 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10

= 1/4 + 1/2 - 1/10

= 5/20 + 10/20 - 2/20

= 13/20

=> A = 13/20 : 1/2 = 13/10

Đặt A = 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45

=> 1/2A = 1/4 + 1/6 + 1/12 + 1/20 + 1/30 + ... + 1/72 + 1/90

= 1/4 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/8.9 + 1/9.10

= 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10

= 1/4 + 1/2 - 1/10 

= 5/20 + 10/20 - 2/20 = 13/20

=> A = 13/20 : 1/2 = 13/10

đặt \(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{36}+\frac{1}{45}\)

\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}+\frac{1}{90}\)

\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\)

\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{10}=\frac{13}{20}\)

\(\frac{1}{2}A\times2=A=2\times\frac{13}{20}=\frac{13}{10}\)

Ta co:

\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{72}+\frac{1}{90}\)

\(\Leftrightarrow\frac{1}{2}A=\frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}+\frac{1}{9.10}\)

\(\Leftrightarrow\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(\Leftrightarrow\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{10}=\frac{13}{20}\Rightarrow A=\frac{13}{10}.\)

\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{36}+\frac{1}{45}\)

\(A=\frac{2}{4}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{72}+\frac{2}{90}\)

\(A=\frac{2}{2.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{8.9}+\frac{2}{9.10}\)

\(A=2\left(\frac{1}{2.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(A=2.\frac{2}{5}\)

\(A=\frac{4}{5}\)

~ Học tốt ~ K cho mk nhé! Thank you.

\(\frac{9}{11}\)nha kb đi

lấy (1/3 + 1/15 +1/10 + 1/21 ) + (1/36 + 1/28 + 1/6) + (1/45 + 1/55)

      =  (4/50 + 3/70) + 2/100

      = 7/120 + 2/100

      = 9/220

= 9/11

a: \(=\left(\dfrac{2}{18}-\dfrac{15}{18}-\dfrac{72}{18}\right):\left(\dfrac{21}{36}-\dfrac{1}{36}-\dfrac{360}{36}\right)\)

\(=\dfrac{-85}{18}:\dfrac{-170}{18}\)

\(=\dfrac{85}{170}=\dfrac{1}{2}\)

b: \(=\left(\dfrac{5}{8}-\dfrac{5}{6}-\dfrac{5}{32}+\dfrac{5}{64}\right):\left(1-\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}\right)\)

\(=\dfrac{-55}{192}:\dfrac{3}{8}=\dfrac{-55}{192}\cdot\dfrac{8}{3}=-\dfrac{55}{72}\)

\(S = \frac{1}{3} +\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28} \)

\(S=\frac{1}{3}+\frac{1}{3}.\frac{1}{2}+\frac{1}{5}.\frac{1}{2}+\frac{1}{5}.\frac{1}{3}+\frac{1}{7}.\frac{1}{3}+\frac{1}{7}.\frac{1}{4} \)

\(S=\frac{1}{3}(1+\frac{1}{2})+\frac{1}{5}(\frac{1}{2}+\frac{1}{3})+\frac{1}{7}(\frac{1}{3}+\frac{1}{4})\)

\(S=\frac{1}{3}.\frac{3}{2}+\frac{1}{5}.\frac{5}{6}+\frac{1}{7}.\frac{7}{12}\)

\(S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}\)

\(S=\frac{6}{12}+\frac{2}{12}+\frac{1}{12}\)

\(S=\frac{9}{12}\)

\(S=\frac{3}{4}\)

S=\(\frac{3}{4}\)

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