Question

Tìm \(x\) biết: \(\left(\frac{11}{12}+\frac{11}{12\cdot23}+\frac{11}{23\cdot34}+...+\frac{11}{89\cdot100}\right)+x=\frac{5}{3}\)

Answer 1

1.(11/12+11/23+11/23+11/24+...+11/89+11/100)+x=5/3

1.(11/12+11/100)+x=5/3

77/75+x=5/3

x=5/3-77/75

x=16/25
 

Answer 2

de ot

=> ( 11/12+ 1/12- 1/23+ 1/23- 1/34+...+ 1/89-1/100 ) +x=5/3

=> (11/12+ 1/12-1/100 ) + x=5/3

=> (11/12+ 11/150) + x=5/3

=>99/100 +x = 5/3

=> x = 5/3 - 99/100

=> x= 203 / 300

K dung NHA

Answer 3

Ta có : (\(\frac{11}{12}+\frac{11}{12\times23}+\frac{11}{23\times34}+...+\frac{11}{89\times100}\)) + x =\(\frac{5}{3}\)

=> (\(\frac{11}{1\times12}+\frac{11}{12\times23}+\frac{11}{23\times34}+...+\frac{11}{89\times100}\)) + x =\(\frac{5}{3}\)

=> (\(1-\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+\frac{1}{23}-\frac{1}{34}+...+\frac{1}{89}-\frac{1}{100}\)) + x =\(\frac{5}{3}\)

=> (\(1-\frac{1}{100}\)) + x =\(\frac{5}{3}\)

=> \(\frac{99}{100}\)+ x =\(\frac{5}{3}\)

=> x = \(\frac{5}{3}-\frac{99}{100}=\frac{203}{300}\)

Vậy x = \(\frac{203}{300}\)