10 cách

Ta có: \(1+2+3+...+n=\frac{n.\left(n+1\right)}{2}\)

\(Q=\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+3+...+10}\)

\(Q=\frac{1}{\frac{2.\left(2+1\right)}{2}}+\frac{1}{\frac{3.\left(3+1\right)}{2}}+....+\frac{1}{\frac{10.\left(10+1\right)}{2}}\)

\(Q=\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+....+\frac{1}{\frac{10.11}{2}}\)

\(Q=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{10.11}\)

\(\frac{1}{2}Q=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{10.11}\)

\(\frac{1}{2}Q=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}=\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)

=>\(Q=\frac{9}{22}.2=\frac{9}{11}\)

\(Q=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{55}\\ \Rightarrow\frac{1}{2}Q=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\)

Tiếp theo tự tính nhé

Câu hỏi của ho thi mai linh - Toán lớp 6 - Học toán với OnlineMath

Câu hỏi của Đinh Bảo Châu Thi - Toán lớp 6 - Học toán với OnlineMath

Câu hỏi của linh - Toán lớp 6 - Học toán với OnlineMath

1/8-1/2

msc=8

1/2=4/8

1/2-4/8=-3/8

\(\frac{1}{8}-\frac{1}{2}=\frac{1}{8}-\frac{4}{8}=\frac{1-4}{8}=\frac{3}{8}\)

\(-\frac{11}{12}-\left(-1\right)=-\frac{11}{12}+1=-\frac{11}{12}+\frac{12}{12}=\frac{-11+12}{12}=\frac{1}{12}\)

tích nha

cái bài dó mk chỉ giải cho bạn theo kiểu bấm máy thôi chứ trình bày sợ bạn không hiểu

Bạn ghi cách giải giúp mk đi ko sao đâu. Cám ơn bạn trước

Bài làm 

\(D=\frac{6}{3,5}+\frac{6}{5.7}+...+\frac{6}{21.23}\)

\(D=3.\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{21.23}\right)\)

\(D=3.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{21}-\frac{1}{23}\right)\)

\(D=3.\left(\frac{1}{3}-\frac{1}{23}\right)\)

\(D=3.\frac{20}{69}\)

\(D=\frac{20}{23}\)

Học tốt 

Bài làm 

 \(D=\frac{6}{3.5}+\frac{6}{5.7}+...+\frac{6}{21.23}\)

\(D=3.\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{21.23}\right)\)

\(D=3.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{21}-\frac{1}{23}\right)\)

\(D=3.\left(\frac{1}{3}-\frac{1}{23}\right)\)

\(D=3.\frac{20}{69}\)

\(D=\frac{20}{23}\)

   \(E=\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\)

\(E=10.\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)\)

\(E=10.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)\)

\(E=10.\left(\frac{1}{11}-\frac{1}{55}\right)\)

\(E=10.\frac{4}{55}\)

\(E=\frac{8}{11}\)

     \(G=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)

\(G=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

\(G=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

\(G=\frac{1}{1}-\frac{1}{100}\)

\(G=\frac{99}{100}\)

Nhớ k cho m nha 

\(A=2.\left(\dfrac{1}{2.5}+\dfrac{1}{5.8}+...+\dfrac{1}{95.98}\right)\)

\(A=\dfrac{2}{3}\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+....+\dfrac{3}{95.98}\right)\)

\(A=\dfrac{2}{3}\left(\dfrac{1}{2}-\dfrac{1}{98}\right)\)

\(A=\dfrac{2}{3}\dfrac{24}{49}=\dfrac{16}{49}\)

Ta có: A=\(\dfrac{2}{2.5}+\dfrac{2}{5.8}+\dfrac{2}{8.11}+...+\dfrac{2}{95.98}\)

\(\Rightarrow A=\dfrac{3}{2}.\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+...+\dfrac{3}{95.98}\right)\)\(\Rightarrow A=\dfrac{3}{2}.\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{95}-\dfrac{1}{98}\right)\)\(\Rightarrow A=\dfrac{3}{2}.\left(\dfrac{1}{2}-\dfrac{1}{98}\right)\)

\(\Rightarrow A=\dfrac{3}{2}.\left(\dfrac{49}{98}-\dfrac{1}{98}\right)\)

\(\Rightarrow A=\dfrac{3}{2}.\dfrac{48}{98}\)

\(\Rightarrow A=\dfrac{3.2.2.12}{2.2.49}\)

\(\Rightarrow A=\dfrac{36}{49}\)

tick cho minh nha 

Cho tớ hỏi x , y thuộc Z hay thuộc N