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

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

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

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

Tới bước này cậu rút hết thì ta sẽ còn

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

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

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

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

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

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

bat ki ai tra loi dung mk deu k

a.(-2/3+3/7) : 4/5 + (-1/3+4/7) : 4/5

= [(-2/3 + 3/7) + (-1/3 + 4/7)] : 4/5

= [(-2/3 + (-1/3) + (3/7 + 4/7)] : 4/5

= [-1 + 1] : 4/5

= 0 : 4/5

= 0   

a) \(\left(\frac{-2}{3}+\frac{3}{7}\right).\frac{5}{4}+\left(\frac{-1}{3}+\frac{4}{7}\right).\frac{5}{4}\)

=\(\left(\frac{-2}{3}+\frac{-1}{3}+\frac{3}{7}+\frac{4}{7}\right).\frac{5}{4}\)

= \(0.\frac{5}{4}=0\)

b) \(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}+\frac{1}{15}-\frac{2}{3}\right)\)

=\(\frac{5}{9}:\frac{-81}{110}=\frac{-550}{729}\)

=5^3+3^9

=125+19683

=19808

5 x 6 : 5 x 3 + 3 x 2 x 3 x 7 

= 30 : 15 + 126 

= 2 + 126 

= 128

5x6:5x3+3x2x3x7

=5x(6:3)+3x2x3x7

=5x2+126

=10+126

=136

a)1+(-2)+3+(-4)+...+19+(-20)

=[1+(-2)]+[3+(-4)]+...+[19+(-20)]

=(-1)+(-1)+...+(-1)=(-1)x10=-10

b)1-2+3-4+....+99-100

=(1-2)+(3-4)+...+(99-100)

=(-1)+(-1)+...+(-1)

=(-1)x50=-50

a) 1+(-2)+3+(-4)+...+19+(-20)

=[1+(-2)] + [3+(-4)]+.....+[19+(-20)]

=(-1)+(-1)+....+(-1)            (10 số hạng -1)

=(-1).10

=-10

 \(\dfrac{5}{7}< \dfrac{x}{5}< 1\) 

\(\dfrac{5\times5}{7\times5}< \dfrac{7\times x}{7\times5}< \dfrac{35}{35}\)

\(\dfrac{25}{35}< \dfrac{7\times x}{35}< \dfrac{35}{35}\)

\(25< 7\times x< 35\)

\(\dfrac{25}{7}< x< \dfrac{35}{7}\)

\(\dfrac{25}{7}< x< 5\)

\(3< x< 5\) (x is the natural number)  

x=4 

 answer please

a) 100 - 99 + 98 - 87 + 96 - 95 + ... + 4-3 + 2

dãy số trên có số số hạng  ( bớt 2 ) là :

( 100 - 3 ) : 1 + 1 = 98 ( số số hạng )

= 1 +1+1+...+1+2

= 1 x 98 + 2

= 98 + 2

= 100

b) 100 - 5 -5 - .... ( có 20 chữ số 5 )

= 100 - ( 5 x 20 )

= 100 - 100

= 0

c) 99 - 9 - 9 -... ( có 11 chữ số 9 )

= 99 - 9 x 11 

= 99 - 99

= 0