Question

3/4+1/1.2+1/2.3+1/3.4+........+1/99.100

Answer 1

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Answer 2

\(\frac{3}{4}+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.........+\frac{1}{99.100}\)

\(=\frac{3}{4}+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{3}{4}+1-\frac{1}{100}=\frac{87}{50}\)

Answer 3

Đề bài: Tính

\(\frac{3}{4}+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=\frac{3}{4}+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{3}{4}+1-\frac{1}{100}\)

\(=\frac{3}{4}+\frac{99}{100}=\frac{75}{100}+\frac{99}{100}=\frac{174}{100}=\frac{87}{50}\)

Answer 4

\(\frac{3}{4}+\frac{1}{1.2}+...+\frac{1}{99.100}=\frac{3}{4}+\frac{2-1}{1.2}+....+\frac{100-99}{99.100}=\frac{3}{4}+1-\frac{1}{2}+...-\frac{1}{100}\)

\(=\frac{7}{4}-\frac{1}{100}=\frac{174}{100}\)