\(\dfrac{1}{1\times5}+\dfrac{1}{5\times9}+...+\dfrac{1}{45\times49}\)

\(=\dfrac{1}{4}\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+...+\dfrac{4}{45\times49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{45}-\dfrac{1}{49}\right)\)

\(=\dfrac{1}{4}\times\left(1-\dfrac{1}{49}\right)=\dfrac{1}{4}\times\dfrac{48}{49}=\dfrac{12}{49}\)

a) \(\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{47.49}=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+......+\frac{2}{47.49}\right)=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{47}-\frac{1}{49}\right)=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\left(1-\frac{1}{49}\right)=\frac{24}{x+4}\)

\(\Rightarrow\frac{1}{2}.\frac{48}{49}=\frac{24}{x+4}\)

\(\Rightarrow\frac{24}{49}=\frac{24}{x+4}\)

\(\Rightarrow x+4=49\Rightarrow x=45\)

\(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{47.49}=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{47.49}\right)=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{47}-\frac{1}{49}\right)=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{49}\right)=\frac{24}{x+4}\Leftrightarrow A=\frac{1}{2}.\frac{48}{49}=\frac{24}{x+4}\)

\(\Rightarrow A=\frac{24}{49}=\frac{24}{x+4}\Leftrightarrow x=49-4=45\)

Bài b) hình như sai đề thì phải đó bạn.

a)ta co \(\frac{1}{1.3}+\frac{1}{3.5}+..+\frac{1}{47.49}=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{47}-\frac{1}{49}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{49}\right)=\frac{24}{49}=\frac{24}{x+4}\)\(\Rightarrow49=x=4\Rightarrow x=45\)

b)ta co \(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{97.101}=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}=\frac{2x+4}{101}\Rightarrow100=2x+4\Rightarrow x=48\)

A = 4/1 x 5 + 4/5 x 9 + 4/9 x 13 + .... + 4/91 x 95 + 4/95 x 99

A = 1 - 1/5 + 1/5 -1/9 + 1/9 - 1/13 + .... + 1/91 - 1/95 + 1/95 - 1/99

A = 1 - 1/99

A = 98/99

B = 1/6 + 1/12 + 1/20 + ... + 1/132

B = 1/2 x 3 + 1/3 x 4 + 1/4 x 5 + ... + 1/11 x 12

B = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/11 - 1/12 

B = 1/2 - 1/12 

B = 5/12

\(\left(2007-2005\right)+\left(2003-2001\right)+...+\left(7-5\right)+\left(3-1\right)\)

\(=2+2+...+2\)

\(=2.1004=2008\)

\(\dfrac{1}{1.5};\dfrac{1}{5.9};\dfrac{1}{9.13};\dfrac{1}{13.17}\)

Lời giải:

$12A=1.5.12+5.9.(13-1)+9.13(17-5)+13.17(21-9)+....+77.81(85-73)+81.85(89-77)$

$=60+(5.9.13+9.13.17+13.17.21+...+77.81.85+81.85.89)-(1.5.9+5.9.13+9.13.17+...+73.77.81+77.81.85)$

$=60+81.85.89 - 1.5.9=612780$

A = 1.5 + 5.9 + 9.13 + ... + 81.85

A = \(\dfrac{12}{12}\)(1.5 + 5.9 + 9.13 + 81.85)

A = \(\dfrac{1}{12}\).(1.5.12 + 5.9.12.+ 9.13.12 + ...+ 81.85.12]

A = \(\dfrac{1}{12}\).[1.5.(9 + 3) + 5.9.(13 - 1) + 9.13.(17 - 5) +...+ 81.85.(89 - 77)]

^{A = \(\dfrac{1}{12}\).[1.5.9 + 1.3.5 + 5.9.13 - 5.9.1 + 9.13.17 - 9.13.5 + ...+ 81.85.89 - 81.85.77]}

A = \(\dfrac{1}{12}\).[1.3.5 + 81.85.89]

A = \(\dfrac{1}{12}\).[15 + 612765]

A = \(\dfrac{1}{12}\).612780

A = 51065

làm bừa thui,ai tích mình mình tích lại

Số số hạng là : 

Có số cặp là :

50 : 2 = 25 ( cặp )

Mỗi cặp có giá trị là :

99 - 97 = 2 

Tổng dãy trên là :

25 x 2 = 50

Đáp số : 50

A = 1.5 + 5.9 + 9.13 + ...+ 41.45

A = \(\dfrac{12}{12}\).(1.5 + 5.9 + 9.13 +...+ 41.45)

A = \(\dfrac{1}{12}\).(1.5.12 + 5.9.12 + 9.13.12 + ... + 41.45.12)

^{A = \(\dfrac{1}{12}\).[1.5.(9 + 3) + 5.9.(13 - 1) + 9.13.(17 - 5) + ... + 41.45.(49 - 37)]} 

^{A = \(\dfrac{1}{12}\)[1.5.9 + 1.5.3 + 5.9.13 - 1.5.9 + 9.13.17 - 5.9.13 +...+41.45.49 - 41.45.37]}

A =\(\dfrac{1}{12}\).[1.5.3  + 41.45.49]

A = \(\dfrac{1}{12}\).[15 + 90405]

A = \(\dfrac{1}{12}\).90420

A = 7535

^.

)chứng tỏ

a)1/1x2+1/2x3+...+1/9x10 <1

b)1/1x2+1/2x3+...+1/99x100 <1

a)4/1x5+1/5x9+1/9x13+1/13x17+1/17x21<1

Lưu ý:"x" là phép nhân

Toán lớp 6

ái tích mình tíc lại nhà 

CÂU a đề bài nó sao sao đó

mà gợi ý cho bạn ....bạn tính tổng đó ra bao nhiêu rồi đem so sánh cho 1

a) 1/1x5 + ... + 1/21x25

= 4 x (1-1/5 + 1/5 - 1/9 + ... + 1/21 - 1/25)

= 1/4 x (1 - 1/25)

= 1/4 x 24/25

= 6/25