đỉ mẹ, đỉ má, cái lồn, con cặc.

\(120\left(\dfrac{1}{24.25}+\dfrac{1}{25.26}+...+\dfrac{1}{29.30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}+\dfrac{1}{26}+...+\dfrac{1}{29}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120.\dfrac{1}{120}+x=\dfrac{1}{3}\)

\(\Rightarrow1+x=\dfrac{1}{3}\)

\(\Rightarrow x=-\dfrac{2}{3}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}=\frac{1}{5}-\frac{1}{25}=\frac{4}{25}\)

1/5.6+1/6.7+1/7.8+...+1/24.25

= 1/5-1/6+1/6+1/7-1/8+...+1/24-1/25

= 1/5-1/25

= 5/25-1/25

= 4/25

k mik nhé mọi người

(1/24.25 + 1/25.26 + ... + 1/29.30) . 120 + x : 1/3 = -4

(1/24 - 1/25 + 1/25 - 1/26 + ... + 1/29 - 1/30) . 120 + x . 3 = -4

(1/24 - 1/30) . 120 + x . 3 = -4

(5/120 - 4/120) + x . 3 = -4

=> 1/120 . 120 + x . 3 = -4

=> 1 + x . 3 = -4

=> x . 3 = -4 - 1

=> x . 3 = -5

=> x = -5/3

Vậy x = -5/3

{1\24.25 + 1\25.26 +...+ 1\29.30} .120+x:1\3 = -4

\((\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}).120+y:\frac{1}{3}=-4\)

Ta có: \(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\)

\(=\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\)

\(=\frac{1}{24}-\frac{1}{30}\)

\(=\frac{1}{120}\)

Thay vào ta có: \(\frac{1}{120}.120+y:\frac{1}{3}=-4\)

\(\implies 1+y:\frac{1}{3}=-4\)

\(\implies y:\frac{1}{3}=-5\)

\(\implies y=-5.\frac{1}{3}\)

\(\implies y=\frac{-5}{3}\). Vậy \(y=\frac{-5}{3}\)

~ Học tốt a~

\(\left(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\right).120+y:\frac{1}{3}=-4\)

\(\Rightarrow\left(\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\right).120+y:\frac{1}{3}=-4\)

\(\Rightarrow\left(\frac{1}{24}-\frac{1}{30}\right).120+y:\frac{1}{3}=-4\)

\(\Rightarrow\frac{1}{120}.120+y:\frac{1}{3}=-4\)

\(\Rightarrow1+y:\frac{1}{3}=-4\)

\(\Rightarrow y:\frac{1}{3}=-4-1\)

\(\Rightarrow y:\frac{1}{3}=-5\)

\(\Rightarrow y=-5.\frac{1}{3}\)

\(\Rightarrow y=\frac{-5}{3}\)

Vậy  \(y=\frac{-5}{3}\)

_Chúc bạn học tốt_

Ta có : \(\dfrac{x^2}{5.6}\text{=}\dfrac{x^2}{5}-\dfrac{x^2}{6}\)

\(\dfrac{x^2}{6.7}\text{=}\dfrac{x^2}{6}-\dfrac{x^2}{7}\)

\(...\)

\(\dfrac{x^2}{24.25}\text{=}\dfrac{x^2}{24}-\dfrac{x^2}{25}\)

\(\Rightarrow\) biểu thức chỉ còn :

\(\dfrac{x^2}{5}-\dfrac{x^2}{25}\text{=}\dfrac{5x^2-x^2}{25}\text{=}\dfrac{4x^2}{25}\)

Lời giải:

\(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}=\frac{25-24}{24.25}+\frac{26-25}{25.26}+...+\frac{30-29}{29.30}\)

\(=\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\)

\(=\frac{1}{24}-\frac{1}{30}=\frac{1}{120}\)

Vậy:

\(\frac{1}{120}.120+x:\frac{1}{3}=-4\)

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

\(x:\frac{1}{3}=-5\)

\(x=-15\)

\(\left(\dfrac{1}{24.25}+\dfrac{1}{25.26}+...+\dfrac{1}{29.30}\right).120+x:\dfrac{1}{3}=-4\) 

\(\left(\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{26}+...+\dfrac{1}{29}-\dfrac{1}{30}\right).120+x:\dfrac{1}{3}=-4\) 

                              \(\left(\dfrac{1}{24}-\dfrac{1}{30}\right).120+x:\dfrac{1}{3}=-4\) 

                                            \(\dfrac{1}{120}.120+x:\dfrac{1}{3}=-4\) 

                                                        \(1+x:\dfrac{1}{3}=-4\) 

                                                               \(x:\dfrac{1}{3}=-4-1\) 

                                                               \(x:\dfrac{1}{3}=-5\) 

                                                                     \(x=-5.\dfrac{1}{3}\) 

                                                                     \(x=\dfrac{-5}{3}\)