\(S=3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\\ 2S=6+3+\dfrac{3}{2}+...+\dfrac{3}{2^8}\\ 2S-S=\left(6+3+\dfrac{3}{2}+...+\dfrac{3}{2^8}\right)-\left(3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\right)\\ S=6-\dfrac{3}{2^9}\\ S=6-\dfrac{3}{512}\\ S=5\dfrac{509}{512}\)

câu hỏi đâu bạn , nếu bạn cần các câu tính giá trị của biểu thức thì lên trang vndoc để tham khảo nhé !

* Chúc bạn học tốt !

Vẫn ko được ah ?

A = 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132
A = 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 + 1/11.12
A = 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12
A = 1/4 - 1/12 (Cứ hai thằng cạnh nhau cộng lại bằng 0, chỉ còn thằng đầu và thằng cuối)
A = (3 - 1)/12
A = 2/12
A = 1/6

\(A=\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}+\dfrac{1}{10.11}+\dfrac{1}{11.12}\)

\(A=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}\)\(A=\dfrac{1}{5}-\dfrac{1}{12}\)

\(A=\dfrac{12}{60}-\dfrac{5}{60}=\dfrac{7}{60}\)

thiếu đề 

A = \(\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\)

=> A = \(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}+\dfrac{1}{10.11}+\dfrac{1}{11.12}\)

=> A = \(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{12}\)

=> A = \(\dfrac{1}{5}-\dfrac{1}{12}\)

=> A = \(\dfrac{7}{60}\)

Vậy A = \(\dfrac{7}{60}\)

Ta có:

A = \(\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\)

= \(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}+\dfrac{1}{10.11}+\dfrac{1}{11.12}\)

= \(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}\)

= \(\dfrac{1}{5}-\dfrac{1}{12}\) = \(\dfrac{7}{60}\)

\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)

   \(=3\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)

    \(=3\left(2-1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^8}-\frac{1}{2^9}\right)\)

    \(=3\left(2-\frac{1}{2^9}\right)=6-\frac{3}{2^9}=6-\frac{3}{512}=\frac{3069}{512}\)

Quy luật của nó là gì vậy sao lại 2+2²+.....+2⁸ hoặc 2¹⁰

Mà bạn lại ghi là 2⁹ quy luật của nó là gì 

_{\(\frac{7}{60}\)}

A=1/30+1/42+1/56+1/72+1/90+1/110+1/132

A=1/5.6+1/6.7+1/7.8+1/8.9+1/9.10+1/10.11+1/11.12

A=1/5-1/6+1/6-1/7+1/7-1/8+...-1/11+1/12

A=1/5-1/12

A=7/60

Vậy A= 7/60