Question

Tính nhanh :

\(C=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

 

Answer 1

C = \(\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-.....-\frac{1}{2.1}\)

C = \(\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{99.100}\right)\)

C = \(\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)

C = \(\frac{1}{100}-\left(1-\frac{1}{100}\right)=\frac{1}{100}-\frac{99}{100}\)

C = \(\frac{-49}{50}\)

Answer 2

-49/50

Answer 3

=>\(C=\frac{1}{100}-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{99\cdot100}\right)\)

=>\(C=\frac{1}{100}-\left(1-\frac{1}{100}\right)\)

=>\(C=\frac{1}{100}-\frac{99}{100}=-\frac{98}{100}=-\frac{49}{50}\)

Vậy......

Answer 4

C=đã cho

=>\(C=\frac{1}{100}-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{99\cdot100}\right)\)

=>\(C=\frac{1}{100}-\left(1-\frac{1}{100}\right)\)

=>\(C=1-\frac{99}{100}=-\frac{98}{100}=-\frac{49}{50}\)

Vậy......

Answer 5

 

C = 1/100 - 1/100.99 - 1/99.98 - 1/98.97 - ... - 1/3.2 - 1/2.1

C = 1/100 - ( 1/100.99 + 1/99.98 + 1/98.97 + ... + 1/3.2 + 1/2.1)

C = 1/100 - ( 1/1.2 + 1/2.3 + ... + 1/97.98 + 1/98.99 + 1/99.100)

C = 1/100 - ( 1 - 1/2 + 1/2 - 1/3 + .... + 1/97 - 1/98 + 1/98 - 1/99 + 1/99 - 1/100)

C = 1/100 - ( 1 - 1/100)

C = 1/100 - 99/100

C = -98/100 = -49/50