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(1-1/2) x (1-1/3) x .... x (1-1/100)
= 1/2 x 2/3 x ... x 99/100
= 1x2x...x99/2x3x..x100
= 1/ 100
a, \(\frac{3}{5}+25-\frac{1}{5}\)
\(=\left(\frac{3}{5}-\frac{1}{5}\right)+25\)
\(=\frac{2}{5}+25\)
\(=25\frac{2}{5}\)
\(=25,4\)
b, \(13.3.32,27+67,63.39\)
\(=39.32,27+67,63.39\)
\(=39\left(32,37+67,63\right)\)
\(=39.100\)
\(=3900\)
c, \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{99}{100}\)
\(=\frac{1}{100}\)
Tìm X
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\)
\(=\frac{1}{5}\)
\(\Rightarrow x-100=\frac{1}{5}\)
\(x=\frac{1}{5}+100\)
\(x=\frac{1}{5}+\frac{500}{5}\)
\(x=\frac{501}{5}\)
Ta có 1-1/2 =1/2
1-1/3=2/3
1-1/4=3/4
.......
1- 1/100=99/100
=> P= 1/2x2/3x3/4x....x99/100
= ( 1x2x3x...x 99)/ (2x3x4x...x100)
=1/1000
a) ta thấy 1/2x3 + 1/3x4 + 1/4 x 5 + ...... + 1/a x ( a + 1 ) = 1/2 - 1/3 + 1/3 -1/4 +............+ 1/a - 1/a+1 = 49/100
1/2 - 1/a+1= 49/100
1/a+1=1/2 - 49/100
1/a + 1= 1/100
a + 1= 100
a= 100 - 1
a= 99
b) ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16) x ..... x (1 - 1/625)
= 3/4 x 8/9 x 15/16 x...........x 575/576x 624/625 = 1x3/1x4 x 2x4/ 3x3 x 3x5/4 x 4x.................x 23x 25/ 24 x 24 x 24x26/ 25x25
= ( 1/1 x 2/3 x 3/4 x 4/5 x .................x 23/24 x 24/25= 1x2x3x4x..............23x24/ 1 x 3 x 4 x5x............24x25=2/25)
( 3/5 x 4/3 x 5/4 x 6/5x.............x 25/24 x 26/25= 3 x 4 x 5x 6 x ............x 25x 26/ 5 x 3 x 4 x 5x............x 24 x 25= 26/5)
2/25 x 26/5= 52/30= 26/25
(1-1/2)*(1-1/2)*...(1-100)
1-1/3=2/3
1-1/4=3/4
............................
1-1/100=99/100
=1/2*2/3*3/4*....99/100
(1*2*3*4*....*99)/(2*3*4*...*100)
=1/100
=>1/100
học tốt
a)=1/2*2/3......*19/20
=1/20
b)=3/2*4/3......*2008/2007
=3/2007
à là [1 - 1/2018] nhé chưa không phải [1 - 1/100] đâu