Question

A = 9/1*2+9/2*3+9/3*4+...+9/98*99+9/99*100

 

Answer 1

A=9/1.2+9/2.3+9/3.4+.....+9/98.99+9/99.100

  =9.(1/1.2+1/2.3+1/3.4+....+1/98.99+1/99.100

 =9.(1/1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100)

 =9.(1/1-1/100)

 =9.99/100

 =891/100

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Answer 2

\(A=9.\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)\)

\(=9.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=9.\left(1-\frac{1}{100}\right)\)

\(=9.\frac{99}{100}\)

\(=\frac{891}{100}\)

Answer 3

A=9/1.2+9/2.3+9/3.4+.....+9/98.99+9/99.100

 

  =9.(1/1.2+1/2.3+1/3.4+....+1/98.99+1/99.100

 

 =9.(1/1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100)

 

 =9.(1/1-1/100)

 

 =9.99/100

 

 =891/100