55/56

mình cần kết quả

nhầm nhầm mình cần bài giải

\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{56}-\dfrac{1}{67}\)

\(=1-\dfrac{1}{67}=\dfrac{66}{67}\)

Từng câu hay toán bình dương zậy

\(\dfrac{1}{1\times2}+\dfrac{2}{2\times4}+\dfrac{3}{4\times7}+\dfrac{4}{7\times11}+....+\dfrac{11}{56\times67}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+....+\dfrac{1}{56}-\dfrac{1}{67}\)

\(=1-\dfrac{1}{67}\)

\(=\dfrac{1}{66}\)

biể thức trên = 1/1 - 1/2 + 1/2 - 1/4 + 1/7 +.....+ 1/11 - 1/67

= 1/1 - 1/67 = 66/67

\(E=\dfrac{1}{1\times2}+\dfrac{2}{2\times4}+\dfrac{3}{4\times7}+\dfrac{4}{7\times11}+\dfrac{5}{11\times16}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}\)
\(=1-\dfrac{1}{16}=\dfrac{15}{16}\)
#kễnh

A=1/1-1/2+1/2-1/4+1/4-1/7+1/7-1/11+1/11-1/16+1/16-1/22+1/22-1/29

A=1/1-1/29

A=28/29

=45/46

1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 +...+ 8/29x37 + 9/37x46 

=2-1/1x2+4-2/2x4+...+46-37/37x46

=1-1/2+1/2-1/4+...+1/37-1/46

=1-1/46

=45/46

`#``\text{Lócc}`

`***` chấm là nhân.

\(\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+\dfrac{4}{7.11}+...+\dfrac{8}{29.37}+\dfrac{9}{37.46}\\ =\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+..+\dfrac{1}{29}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{46}\\ =\dfrac{1}{1}-\dfrac{1}{46}\\ =\dfrac{46}{46}-\dfrac{1}{46}\\ =\dfrac{45}{46}\)

Gọi biểu thức trên là A, ta có:

A = 1/1x2 + 2/2x4 + 3/4x7 + 4/7x11 + 5/11x16

A = 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/7 + 1/7 - 1/11 + 1/11 - 1/16

A = 1 - 1/16 = 15/16

Đặt \(A=\frac{1}{2}+\frac{2}{2\cdot4}+\frac{3}{4\cdot7}+\frac{4}{7\cdot11}+\frac{5}{11\cdot16}\)

\(\Rightarrow A=\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}\)

\(\Rightarrow A=1-\frac{1}{16}\)

\(\Rightarrow A=\frac{15}{16}\)

k đúng cho mình nhé bạn nhé

a=4099/308

b=2/5/186

giup minh nhe

Chị sẽ giúp em nốt mấy bài này, em còn nhận ra chị ko vậy?

\(A=\frac{2}{1x2}+\frac{2}{2x3}+\frac{2}{3x4}+...+\frac{2}{99x101}\)

\(A=2x\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{99x101}\right)\)

\(A=2x\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(A=2x\left(1-\frac{1}{101}\right)=2x\frac{100}{101}=\frac{200}{101}\)

------------------------------

\(B=\left(1+\frac{1}{2}\right)x\left(1+\frac{1}{3}\right)x\left(1+\frac{1}{4}\right)x...x\left(1+\frac{1}{2016}\right)\)

\(B=\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x...x\frac{2017}{2016}\) (rút gọn từ trên tử xuống dưới mẫu nhé)

\(B=\frac{2017}{2}\)

-------------------------------

\(C=\frac{3}{1x4}+\frac{3}{4x7}+\frac{3}{7x10}+...+\frac{3}{64x67}\)

\(C=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{64}-\frac{1}{67}\)

\(C=1-\frac{1}{67}=\frac{67}{67}-\frac{1}{67}=\frac{66}{67}\)

--------------------------------

\(D=\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x...x\left(1-\frac{1}{20}\right)\)

\(D=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...x\frac{19}{20}\)(chỗ này cũng rút gọn từ trên tử xuống dưới mẫu)

\(D=\frac{1}{20}\)

Đề  phải như này nhé

\(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+......+\frac{2}{99.100}\)

\(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{99.100}\right)\)

  \(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\right)\)

   \(=2.\left(1-\frac{1}{100}\right)\)

    \(=2.\frac{99}{100}\)