Question

[o0o Aikatsu_Mikuru_Mizuki o0o]

Câu 5 : Tính nhanh :

A = \(\frac{2019}{2}\)+\(\frac{2019}{6}\)+ \(\frac{2019}{12}\)+\(\frac{2019}{20}\)+\(\frac{2019}{30}\)+ ... +\(\frac{2019}{2018.2019}\)

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ai nhanh mik tick

Answer 1

[Kẻ Dấu Mặt]

\(A=\frac{2019}{2}+\frac{2019}{6}+\frac{2019}{12}+....+\frac{2019}{2018.2019}\)

   \(=\frac{2019}{1}.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2018.2019}\right)\)

   \(=\frac{2019}{1}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2019}\right)\)

   \(=\frac{2019}{1}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+....+\frac{1}{2018}-\frac{1}{2019}\right)\)

   \(=\frac{2019}{1}.\left(1-\frac{1}{2019}\right)\)

   \(=\frac{2019}{1}.\frac{2018}{2019}\)

   \(=2018\)

Answer 2

[nguyen van huy]

\(A=\frac{2019}{2}+\frac{2019}{6}+\frac{2019}{12}+\frac{2019}{20}+\frac{2019}{30}+\frac{2019}{2018.2019}\)

\(A=\frac{2019}{1.2}+\frac{2019}{2.3}+\frac{2019}{3.4}+\frac{2019}{4.5}+\frac{2019}{5.6}+...+\frac{2019}{2018.2019}\)

\(A=2019.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2018.2019}\right)\)

\(A=2019.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2018}-\frac{1}{2019}\right)\)

\(A=2019.\left(1-\frac{1}{2019}\right)\)\(=2019.\frac{2018}{2019}=2018\)

Vậy A = 2018 

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