Question

[Rin cute]

Tính hợp lý : 4/5+44/55+116/117+220/221+356/357

Answer 1

[NgườiConBíẨn]

\(\frac{4}{5}+\frac{44}{55}+\frac{116}{117}+\frac{220}{221}+\frac{356}{357}\)

\(=\left(1-\frac{1}{5}\right)+\left(1-\frac{1}{55}\right)+\left(1-\frac{1}{117}\right)+\left(1-\frac{1}{221}\right)+\left(1-\frac{1}{357}\right)\)

\(=1.5+\left(\frac{1}{5}+\frac{1}{55}+\frac{1}{117}+\frac{1}{221}+\frac{1}{357}\right)\)

\(=5+\left(\frac{1}{1.5}+\frac{1}{5.11}+\frac{1}{9.13}+\frac{1}{13.17}+\frac{1}{17.21}\right)\)

\(=5+1-\frac{1}{5}+\frac{1}{5}-\frac{1}{11}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}\)

\(=6+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{13}-\frac{1}{13}\right)+\left(\frac{1}{17}-\frac{1}{17}\right)+\left(\frac{1}{9}-\frac{1}{11}-\frac{1}{21}\right)\)

\(=\frac{4158}{693}+\left(\frac{77}{693}-\frac{63}{693}-\frac{33}{693}\right)\)

\(=\frac{4158}{693}-\frac{19}{693}\)

\(=\frac{4139}{693}=5\frac{674}{693}\)