\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{49\cdot50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-.....+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}\)

\(=\frac{24}{50}=\frac{12}{25}\)

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{49\cdot50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}\)

\(=\frac{12}{25}\)

      \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}\)

\(=\frac{25}{50}-\frac{1}{50}\)

\(=\frac{24}{50}=\frac{12}{25}\)

X x 1/2 = 2/3

X = (2/3) / (1/2) = 4/3

\(x\) \(\times\) \(\dfrac{1}{2}\) = 1 - \(\dfrac{1}{3}\) 

\(x\) \(\times\)\(\dfrac{1}{2}\) = \(\dfrac{2}{3}\)

\(x\)        = \(\dfrac{2}{3}\) : \(\dfrac{1}{2}\)

\(x\)        = \(\dfrac{4}{3}\)

X x 1/2 = 1 - 1/3

X x 1/2 = 2/3

X = 2/3 : 1/2

X = 4/3

\(\dfrac{2}{3}\) : \(\dfrac{1}{4}\) = \(\dfrac{8}{3}\) = \(\dfrac{8\times3}{3\times3}\) = \(\dfrac{24}{9}\); \(\dfrac{5}{9}\)

MSC nhỏ nhất là 36

\(\dfrac{2}{3}=\dfrac{2\times12}{3\times12}=\dfrac{24}{36}\)

\(\dfrac{1}{4}=\dfrac{1\times9}{4\times9}=\dfrac{9}{36}\)

\(\dfrac{5}{9}=\dfrac{5\times4}{9\times4}=\dfrac{20}{36}\)

\(\frac{1}{7}\cdot\frac{2}{3}+\frac{5}{6}:\frac{3}{10}-\frac{2}{3}\cdot\frac{3}{7}\)

\(=\left(\frac{1}{7}\cdot\frac{2}{3}-\frac{2}{3}\cdot\frac{3}{7}\right)+\frac{5}{6}\cdot\frac{10}{3}\)

\(=\frac{2}{3}\cdot\left(-\frac{2}{7}\right)+\frac{5}{3}\cdot\frac{5}{3}\)

\(=-\frac{4}{21}+\frac{25}{6}=\frac{167}{42}\)

Xin lỗi không nhanh được 

Bạn ơi câu này trả lời r mà

Ta có 1 + 2 + 3 + ... + x = aaa

<=> x(x + 1) : 2 = a x 111

<=> x(x + 1) = a.222

Vì aaa là số có 3 chữ số 

=> 0 < a < 10 (a \(\inℕ^∗\)) 

Thử a từ 1 đến 9 ta tìm được a = 6 thỏa mãn 

Thật vậy x(x + 1) = a.222

<=> x(x + 1) = 6.222

<=> x(x + 1) = 1332

<=> x(x + 1) = 36.37 

<=> x = 36

Vậy x = 36 ; a = 6 

thank nha !

1+2 . (25 + 9) - 4 MŨ 3 

= 1 + 2 . 34 - 64

= 1 + 68 - 64

= 69 - 64

= 5

Cảm ơn bạn nha ^^

ko có j

1-3+5-7+...+21-23
=(1-3)+(5-7)+...+(21-23)
Tổng số cặp là:
[(23-1):2+1]:2=6
Nháp: [(23-1):2+1]:2=(22:2+1):2=12:2=6
=1-3=-2=-2*6=-12
Đây nha bạn.
Chúc bạn học tốt!

\(1-3+5-7+...+21-23\)

\(=\left(1+5+9+13+17+21\right)-\left(3+7+11+15+19+23\right)\)

\(=\left[\left(21-1\right):2+1\right].\left(21+1\right):2-\left[\left(23-3\right):2+1\right].\left(23+3\right):2\)

\(=11.11-11.13\)

\(=121-143\)

\(=-22\)