Question

Tính tổng

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)

Answer 1

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...........+\frac{1}{37.38.39}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+..........+\frac{1}{37.38}-\frac{1}{38.39}\)

\(=\frac{1}{1.2}-\frac{1}{38.39}\)

\(=\frac{1}{2}-\frac{1}{1482}\)

\(=\frac{741}{1482}-\frac{1}{1482}\)

\(=\frac{370}{741}\)

Answer 2

= \(\frac{38}{39}\)

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