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\(=\left[16\cdot\left(\dfrac{1}{13}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{27}+...+\dfrac{1}{62}-\dfrac{1}{69}\right)\right]:\dfrac{-112}{897}\)
\(=16\left(\dfrac{1}{13}-\dfrac{1}{69}\right)\cdot\dfrac{-897}{112}\)
\(=-\dfrac{897}{7}\cdot\dfrac{56}{897}=-8\)
Ta có: \(\left(\frac{112}{13.20}+\frac{112}{20.27}+...+\frac{112}{62.69}\right)\)
=\(\left(\frac{112}{13}-\frac{112}{20}+\frac{112}{20}-\frac{112}{27}+...+\frac{112}{62}-\frac{112}{69}\right)\)
112 là tử chung
=>\(112\cdot\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+...+\frac{1}{62}-\frac{1}{69}\right)\)
Rút gọn các phân số cho nhau, ta còn:
\(112.\left(\frac{1}{13}-\frac{1}{69}\right)\)=\(112\cdot\frac{56}{897}=\frac{6272}{897}\)(1)
Ta có: \(\left(\frac{-5}{9\cdot13}-\frac{7}{9\cdot25}-\frac{13}{19\cdot25}-\frac{31}{19\cdot69}\right)\)=\(\left(-\frac{24}{325}-\frac{122}{32775}\right)\)=\(\left(-\frac{1322}{17043}\right)\)(2)
(1);(2) => \(A=\)\(\frac{6272}{897}\)\(:\left(-\frac{1322}{17043}\right)\)\(\)\(=\)\(-\frac{59584}{661}\)
C
\(\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+...+\frac{112}{62.69}\)
= \(16.\left(\frac{7}{13.20}+\frac{7}{20.27}+\frac{7}{27.34}+...+\frac{7}{62.69}\right)\)
= \(16.\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+\frac{1}{27}-\frac{1}{34}+...+\frac{1}{62}-\frac{1}{69}\right)\)
= \(16.\left(\frac{1}{13}-\frac{1}{69}\right)\)
= \(16.\frac{56}{897}\)
= \(\frac{896}{897}\)
\(\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+...+\frac{112}{62.69}\)
\(=16\left(\frac{7}{13.20}+\frac{7}{20.27}+\frac{7}{27.34}+...+\frac{7}{62.69}\right)\)
\(=16\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+...+\frac{1}{62}-\frac{1}{69}\right)\)
\(=16\left(\frac{1}{13}-\frac{1}{69}\right)=\frac{16}{13}-\frac{16}{69}\)
\(16^x=128^4\)