Question

tính tích: P=(1-1/2).(1-1/3).(1-1/4).........(1-1/999).(1-1/1000)

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Answer 1

\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{999}\right)\left(1-\frac{1}{1000}\right)\)

\(P=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{998}{999}\cdot\frac{999}{1000}\)

\(P=\frac{1\cdot2\cdot3\cdot4\cdot...\cdot999}{2\cdot3\cdot4\cdot5\cdot...\cdot1000}\)

\(P=\frac{1}{1000}\)

Answer 2

\(P=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{998}{999}\times\frac{999}{1000}\)

P=1/1000

_Kudo_

Answer 3

\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\cdot.....\cdot\left(1-\frac{1}{999}\right)\left(1-\frac{1}{1000}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot....\cdot\frac{998}{999}\cdot\frac{999}{1000}\)

\(=\frac{1\cdot2\cdot3\cdot....\cdot998\cdot999}{2\cdot3\cdot4\cdot....\cdot999\cdot1000}=\frac{1}{1000}\)

Vậy \(P=\frac{1}{1000}\)