Lưu ý : . là dấu nhân

ai làm đúng , nhanh mình k

bình chọn đúng

\(\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}\)

\(=\frac{8-7}{7\cdot8}+\frac{9-8}{8\cdot9}+\frac{10-9}{9\cdot10}+\frac{11-10}{10\cdot11}+\frac{12-11}{11\cdot12}+\frac{13-12}{12\cdot13}\)

\(=\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}\)

\(=\frac{1}{7}-\frac{1}{13}=\frac{13-7}{7\cdot13}=\frac{6}{91}\)

\(\frac{6}{91}\)nha

co \(\frac{1}{9\cdot10}=\frac{1}{9}-\frac{1}{10}\)

\(\frac{1}{10\cdot11}=\frac{1}{10}-\frac{1}{11}\)

............

\(\frac{1}{x\left(x+1\right)}=\frac{1}{x}-\frac{1}{x+1}\)

nen \(\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+...+\frac{1}{x\left(x+1\right)}\)

\(=\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}-...+\frac{1}{x}-\frac{1}{x+1}\)

=\(\frac{1}{9}-\frac{1}{x+1}\)

2 .  ( \(\frac{1}{9\cdot10}+\frac{1}{10\cdot11}+...+\frac{1}{x\left(x+1\right)}\))

=  2  . ( \(\frac{1}{9}-\frac{1}{x+1}\))  = \(\frac{2}{9}-\frac{2}{x+1}\)

Bạn ơi tim x mà bạn

bo may ko biet

caau hoi tuong tu cungx cos

\(2\left(\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1}{9}\)

\(\Leftrightarrow2\left(\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{1}{9}\)

\(\Leftrightarrow2\left(\frac{1}{9}-\frac{1}{x+1}\right)=\frac{1}{9}\)

\(\Leftrightarrow\frac{1}{9}-\frac{1}{x+1}=\frac{1}{9}\div2\)

\(\Leftrightarrow\frac{1}{9}-\frac{1}{x+1}=\frac{1}{18}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{9}-\frac{1}{18}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{18}\)

\(\Leftrightarrow x+1=18\)

\(\Leftrightarrow x=18-1\)

\(\Leftrightarrow x=17\)

\(\left|x\right|-\frac{3}{4}=\frac{5}{3}\)

\(\Leftrightarrow\left|x\right|=\frac{5}{3}+\frac{3}{4}\)

\(\Leftrightarrow\left|x\right|=\frac{20}{12}+\frac{9}{12}\)

\(\Leftrightarrow\left|x\right|=\frac{29}{12}\)

\(\Leftrightarrow x=\pm\frac{29}{12}\)

Bài 1 :

\(2.\left(\frac{1}{9.10}+\frac{1}{10.11}+...+\frac{1}{x.\left(x+1\right)}\right)\)= \(\frac{1}{9}\)

=> \(\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+...+\frac{1}{x}-\frac{1}{x+1}\)= \(\frac{1}{18}\)

\(\frac{1}{9}-\frac{1}{x+1}=\frac{1}{18}\)

\(\frac{1}{x+1}=\frac{1}{18}\)

=> x + 1 = 18

=> x = 17

vậy x = 17

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{13\cdot14}+\frac{1}{14\cdot15}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{14}-\frac{1}{15}\)

\(=\frac{1}{2}-\frac{1}{15}\)

\(=\frac{13}{30}\)

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cách giải ?