Question

Tìm x biết

\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x.\left(x+3\right)}=\frac{6}{19}\)

Answer 1

1/3.(1-1/4+1/4-1/7+......+1/x-1/(x+3)=6/19

1/3.(1-1/x+3)=6/19

1-1/x+3=6/19:1/3

1-1/x+3=18/19

1/x+3=1-18/19

1/x+3=1/19

=> x+3=19

=>x=19-3

x=16    

Answer 2

Đặt biểu thức là A, ta có:

3A=\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.11}+...+\frac{3}{x\left(x+3\right)}\)

3A=\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+3}\)

3A=1-\(\frac{1}{x+3}\)

A=\(\frac{1}{3}-\frac{3}{x+3}\)

=>\(\frac{1}{3}-\frac{3}{x+3}\)  =\(\frac{6}{19}\) =>x=168

Answer 3

1/3.(1-1/4+1/4-1/7+......+1/x-1/(x+3)=6/19

1/3.(1-1/x+3)=6/19

1-1/x+3=6/19:1/3

1-1/x+3=18/19

1/x+3=1-18/19

1/x+3=1/19

=> x+3=19

=>x=19-3

x=16    

Answer 4

1/3.(3/1.4+3/4.7+3/7.10+...+3/x.(x+3)

1/3.(1/1-1/4+1/4-1/7+1/7-1/10+...+1/x-1/x+3)=6/19

1/3.(1/1-1/x+3)=6/19

1/1-1/x+3=6/19:1/3=6/19.3=18/19

1/x+3=1-18/19=1/19

x+3=19

x=16

Answer 5

k viết lại đề nữa nha :))

=1-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{7}\)+...+\(\frac{1}{x}\)- \(\frac{1}{x+3}\) = \(\frac{6}{19}\)

=1-\(\frac{1}{x+3}\)=\(\frac{6}{19}\)

=) \(\frac{1}{x+3}\)=1-\(\frac{6}{19}\)=\(\frac{13}{19}\)

=)\(\frac{1}{x+3}\):13=\(\frac{13}{19}\):13

=)\(\frac{1}{13x+39}\)=\(\frac{1}{19}\)

=)13x+39 =19=)13x = 19-39= -20

=) x = \(\frac{-20}{3}\)

Answer 6

\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x.\left(x+3\right)}=\frac{6}{19}\)

\(\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}\right)=\frac{6}{19}\)

\(\frac{1}{3}.\left(1-\frac{1}{x+3}\right)=\frac{6}{19}\)

\(\frac{1}{x+3}=\frac{1}{19}\)

x+3=19

x=16

\(\frac{1}{4}-\frac{1}{x+3}=\frac{18}{19}\)

Answer 7

1/1.4+1/4.7+1/7.10+...+1/x.(x+3)=6/19

1/3.[1/1.4+1/4.7+1/7.10+...+1/x.(x+3)=6/19

3/1.4+3/4.7+3/7.10+...+3/x.(x+3)=6/19

1/1-1/4+1/4-1/7+1/7-1/10+...+1/x-1/x+3=6/19

1-1/x+3=6/19

1/x+3=1-6/19

1/x+3=13/19

1/13x+39=1/19

13x+39=19

13x=19-39= -20

x=-20/3