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Lời giải:
Gọi tổng trên là $A$
$A=\frac{1}{\frac{2\times 3}{2}}+\frac{1}{\frac{3\times 4}{2}}+\frac{1}{\frac{4\times 5}{2}}+...+\frac{1}{\frac{100\times 101}{2}}$
$=\frac{2}{2\times 3}+\frac{2}{3\times 4}+\frac{2}{4\times 5}+....+\frac{2}{100\times 101}$
$=2\times (\frac{1}{2\times 3}+\frac{1}{3\times 4}+\frac{1}{4\times 5}+....+\frac{1}{100\times 101})$
$=2\times (\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+\frac{5-4}{4\times 5}+....+\frac{101-100}{100\times 101})$
$=2\times (\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{100}-\frac{1}{101})$
$=2\times (\frac{1}{2}-\frac{1}{101})$
$=1-\frac{2}{101}=\frac{99}{101}$
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![](https://rs.olm.vn/images/avt/0.png?1311)
A\(\frac{7}{15}+\frac{4}{5}=\frac{7}{15}+\frac{12}{15}=\frac{19}{15}\)
B\(\frac{2}{3}-\frac{3}{8}=\frac{16}{24}-\frac{9}{24}=\frac{7}{24}\)
C\(\frac{4}{5}\times\frac{5}{8}=\frac{20}{40}=\frac{1}{2}\)
D\(4:\frac{3}{2}=\frac{4}{1}\times\frac{2}{3}=\frac{8}{3}\)
a: =9/14*7/3+5/6
=3/2+5/6
=9/6+5/6=14/6=7/3
b: =4/7*5/3=20/21