kết quả là 12/125

ủng hộ  mình lên 300 các bạn

bai toan này không đon gian

 {1 - 1/97} *{1 - 1/98}*........* {1 - 1/1000} 

\(\frac{96}{97}\times\frac{97}{98}\times\frac{98}{99}\times\frac{99}{100}\times...\frac{998}{999}\times\frac{999}{1000}\)

 \(\frac{96}{1000}\)

\(\left(1-\frac{1}{97}\right)\times\left(1-\frac{1}{98}\right)\times...\times\left(1-\frac{1}{1000}\right)=\frac{96}{97}\times\frac{97}{98}\times...\times\frac{999}{1000}=\frac{96}{1000}=\frac{12}{125}\)

\(=\frac{96}{97}\cdot\frac{97}{98}\cdot....\cdot\frac{999}{1000}=\frac{96\cdot97\cdot...\cdot999}{97\cdot98\cdot...\cdot1000}=\frac{96\cdot1\cdot...\cdot1}{1\cdot...\cdot1\cdot1000}=\frac{96}{1000}=\frac{12}{125}\)

Bx3=1x3/1x2x3x4+1x3/2x3x4x5+...+1x3/97x98x99x100

Bx3=3/1x2x3x4+3/2x3x4x5+...+3/97x98x99x100

Bx3=1/1x2x3-1/2x3x4+1/2x3x4-1/3x4x5+...+1/97x98x99-1/98x99x100

BX3=1/1x2x3-1/98x99x100

BX3=1/6-1/970200

Bx3=161700/970200-1/970200

Bx3=161399/970200

B=161699/970200:3

B=161699/970200x1/3

B=161699/2910600

\(B=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+....+\frac{1}{97.98.99.100}\)

\(B=\frac{4-1}{1.2.3.4}+\frac{5-2}{2.3.4.5}+...+\frac{100-97}{97.98.99.100}\)

\(B=\frac{1}{3}\cdot\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)

\(B=\frac{1}{3}\cdot\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)\)

\(B=\frac{1}{3}\cdot\frac{161699}{970200}=\frac{161699}{2910600}\)

=96/97x97/98x98/99x...x999/1000

=96/1000

=12/125

(1-1/97)x(1-1/98)x...x(1-1/1000)

=96/97x97/98x...x999/1000 (Mình gạch các tử số giống mẫu số.VD:a/b x b/c=a/c)

=96/1000

=0,096

(1-1/97)*(1-1/98)*...(1-1/1000)

= 96/97*97/98*...*999/1000

= 96/1000 = 49/500

\(\left(1-\frac{1}{97}\right)\left(1-\frac{1}{98}\right)....\left(1-\frac{1}{1000}\right)\)

\(=\frac{96}{97}\times\frac{97}{98}\times....\times\frac{999}{1000}\)

\(=\frac{96\times97\times.....\times999}{97\times98\times....\times1000}\)

\(=\frac{96\times\left(97\times98\times....\times999\right)}{\left(97\times98\times.....\times999\right)\times1000}=\frac{96}{1000}=\frac{12}{125}\)

\(=\frac{96}{97}\times\frac{97}{98}\times...\times\frac{999}{1000}=\frac{96}{1000}=0,096\)

\(=\frac{96}{97}\cdot\frac{97}{98}\cdot...\cdot\frac{999}{1000}=\frac{96\cdot97\cdot...\cdot999}{97\cdot98\cdot...\cdot1000}=\frac{96\cdot1\cdot....\cdot1}{1\cdot1\cdot....\cdot1\cdot1000}=\frac{96}{1000}=\frac{12}{125}\)

96/97x97/98x....x999/1000

=96x97x...x999x1000/97x98x...x999x1000

=96/1000

=12/125