Question

[luuthemanh]

tính 4pghan 2nhan 4 công 4phan 4 nhan6 cộng 4 phần 8 nhân 10 công ... cộng 4 phan18 nhân 20

Answer 1

[I don't need you]

\(\frac{4}{2x4}+\frac{4}{4x4}+\frac{4}{4x6}+\frac{4}{6x8}+\frac{4}{8x10}+...+\frac{4}{18x20}\)

\(=\frac{4}{2}x\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+...+\frac{1}{18}-\frac{1}{20}\right)\)

\(=2x\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=2x\frac{9}{20}=\frac{9}{10}\)

Answer 2

[Nguyễn Thanh Hiền]

\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{18.20}\)

\(=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{18.20}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=2.\frac{9}{20}\)

\(=\frac{9}{10}\)

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