Question

tinh tich p= (1-1/2).(1-1/3).(1-1/4)......(1-1/99)

please help me!!!!!!!!!

Answer 1

\(P=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{99}\right).\)

\(P=\left(\frac{2}{2}-\frac{1}{2}\right).\left(\frac{3}{3}-\frac{1}{3}\right).\left(\frac{4}{4}-\frac{1}{4}\right)....\left(\frac{99}{99}-\frac{1}{99}\right)\)

\(P=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{98}{99}\)

\(P=\frac{1.2.3.4...98}{2.3.4....99}\)

Tới bước này cậu rút hết thì ta sẽ còn

\(P=\frac{1}{99}\)

Vậy  \(P=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{99}\right)=\frac{1}{99}\)

Answer 2

\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\)

\(P=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{98}{99}\)

\(P=\frac{1.2.3...98}{2.3.4...99}\)

\(P=\frac{1}{99}\)

Answer 3

bat ki ai tra loi dung mk deu k

Answer 4

\(P=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\)

\(P=\left(\frac{2}{2}-\frac{1}{2}\right).\left(\frac{3}{3}-\frac{1}{3}\right).\left(\frac{4}{4}-\frac{1}{4}\right)...\left(\frac{99}{99}-\frac{1}{99}\right)\)

\(P=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{98}{99}\)

\(P=\frac{1.2.3...98}{2.3.4...99}\)

Rút gọn những hết số giống nhau thì ta có :

\(P=\frac{1}{99}\)

Answer 5

thank everyone !!!!! 

Answer 6

\(P=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\)

\(\Leftrightarrow P=\left(\frac{2}{2}-\frac{1}{2}\right)\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{4}{4}-\frac{1}{4}\right)...\left(\frac{99}{99}-\frac{1}{99}\right)\)

\(\Leftrightarrow P=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{98}{99}\)

\(\Leftrightarrow P=\frac{1.2.3...98}{2.3.4...99}\)

\(\Leftrightarrow P=\frac{1}{99}\)

Vậy \(P=\frac{1}{99}\)