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\(\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+...+\frac{112}{62.69}\)

Xyz OLM
25 tháng 7 2019 lúc 21:17

\(\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+...+\frac{112}{62.69}\)

\(16.\left(\frac{7}{13.20}+\frac{7}{20.27}+\frac{7}{27.34}+...+\frac{7}{62.69}\right)\)

\(16.\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+\frac{1}{27}-\frac{1}{34}+...+\frac{1}{62}-\frac{1}{69}\right)\)

\(16.\left(\frac{1}{13}-\frac{1}{69}\right)\)

\(16.\frac{56}{897}\)

\(\frac{896}{897}\)

\(\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+...+\frac{112}{62.69}\)

\(=16\left(\frac{7}{13.20}+\frac{7}{20.27}+\frac{7}{27.34}+...+\frac{7}{62.69}\right)\)

\(=16\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+...+\frac{1}{62}-\frac{1}{69}\right)\)

\(=16\left(\frac{1}{13}-\frac{1}{69}\right)=\frac{16}{13}-\frac{16}{69}\)

Edogawa Conan
25 tháng 7 2019 lúc 21:20

Ta có:

\(\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+....+\frac{112}{62.69}\)

\(16.\left(\frac{7}{13.20}+\frac{7}{20.27}+\frac{7}{27.34}+...+\frac{7}{62.69}\right)\)

\(16.\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+\frac{1}{27}-\frac{1}{34}+...+\frac{1}{62}-\frac{1}{69}\right)\)

\(16.\left(\frac{1}{13}-\frac{1}{69}\right)\)

\(16.\frac{56}{897}=\frac{896}{897}\)

Bùi Đức Vinh
25 tháng 7 2019 lúc 21:24

TA CÓ : \(\frac{112}{13.20}\)+\(\frac{112}{20.27}\)+....+\(\frac{112}{62.69}\)

= 16 . (\(\frac{7}{13.20}\)+\(\frac{7}{20.27}\)+....+\(\frac{7}{62.69}\))

=16.(\(\frac{1}{13}\)-\(\frac{1}{69}\))

=\(\frac{16}{13}\)-\(\frac{16}{69}\)=\(\frac{896}{897}\)

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