Question

1/1.3 - 1/2.4 + 1/3.5 - 1/4.6+.....+1/97.99-1/98.100

 

Answer 1

\(\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+...+\frac{1}{97.99}-\frac{1}{98.100}\)

\(=1-\frac{1}{3}-\frac{1}{2}+\frac{1}{4}+\frac{1}{3}-\frac{1}{5}-\frac{1}{4}+\frac{1}{6}+...+\frac{1}{97}-\frac{1}{99}-\frac{1}{98}+\frac{1}{100}\)

\(=1-\frac{1}{2}-\frac{1}{99}-\frac{1}{98}\)

\(=\frac{2327}{4851}\)

Answer 2

Đặt A=1/1.3 - 1/2.4 +1/3.5 -1/4.6 +.....+1/97.99 -1/98.100

     4A= 4/1.3 -4/2.4 +4/3.5 -4/4.6 +.....+4/97.99 -4/98.100

          =(4/1.3 +4/3.5 +...+4/97.99) - (4/2.4 +4/4.6 +...+4/98.100)

          =(1/1 -1/3+1/3-1/5+...+1/97-1/99)-(1/2 -1/4 -....1/98-1/100)

         =(1/1-1/99)-(1/2-1/100)

         4A=98/99 - 99/100

         A= (98/99-99/100) :4

Answer 3

ngắn gọn nhất nè
1/1.3-1/2.4+1/3.5-1/4.6+...+1/97.99-1/98.100 
= 1- 1/3 - 1/2 + 1/4 + 1/3 - 1/5 - 1/4 + 1/6 + ... + 1/97 - 1/99 - 1/98 + 1/100
= 1 - 1/2 - 1/99 - 1/98
= 2327/4851

Answer 4

1/1.3 - 1/2.4 + 1/3.5 - 1/4.6 +...+ 1/97.99 - 1/98.100 

= 1 - 1/3 - 1/2 + 1/4 + 1/3 - 1/5 - 1/4 + 1/6 +...+ 1/97 - 1/99 + 1/98 + 1/100

= 1- 1/2 + 1/99 - 1/98 = 2327/4851

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