\(\frac{1}{2}S=\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+...+\left(\frac{1}{2}\right)^{21}\)

\(\Rightarrow\left(\frac{1}{2}S\right)-S=\left(\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+...+\left(\frac{1}{2}\right)^{21}\right)-\left(\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^2+...+\left(\frac{1}{2}\right)^{20}\right)\)

\(\Rightarrow-\frac{1}{2}S=\left(\frac{1}{2}\right)^{21}-\left(\frac{1}{2}\right)\)

\(\Rightarrow S=\frac{\left(\left(\frac{1}{2}\right)^{21}-\frac{1}{2}\right)}{-\frac{1}{2}}\)

31/29

\(=\frac{-\frac{1}{8}-\frac{27}{64}.4}{-2+\frac{9}{16}-\frac{3}{8}}\)

\(=\frac{-\frac{1}{8}-\frac{27}{16.4}.4}{-2+\frac{9-6}{16}}\)

\(=\frac{-\frac{1}{8}-\frac{27}{16}}{-2+\frac{3}{16}}\)

\(=\frac{-\left(\frac{2+27}{16}\right)}{\frac{-32+3}{16}}\)

\(=\frac{-\frac{29}{16}}{\frac{-29}{16}}\)

\(=1\)

bài này hình như có trong sách Nâng cao phát triển toán 8?

Nhân từng thừa số ở cả tử và mẫu với 16 là ra ý mà

\(A=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{2017^2}\right)\)

\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}...\frac{2016.2018}{2017^2}\)

\(=\frac{2.3^2.4^2.5^2...2016^2.2017.2018}{2^2.3^2.4^2.5^2...2017^2}\)

\(=\frac{2018}{2.2017}=\frac{1009}{2017}\)

lơp 6  ko bt

mk mới học lớp 6 thôi

tk mk nha mk đang âm điểm nè hu hu

\(A=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\cdot\cdot\cdot\left(1-\frac{1}{n^2}\right)\)

\(\Rightarrow A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\cdot\cdot\cdot\left(1-\frac{1}{n^2}\right)\)

\(\Rightarrow A=\frac{3}{4}\cdot\frac{8}{9}\cdot\cdot\cdot\frac{n^2-1}{n^2}\)

\(\Rightarrow A=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\cdot\cdot\frac{\left(n-1\right)\left(n+1\right)}{n\cdot n}\)

\(\Rightarrow A=\frac{\left(1\cdot3\right)\cdot\left(2\cdot4\right)\cdot\cdot\cdot\left[\left(n-1\right)\left(n+1\right)\right]}{\left(2\cdot2\right)\cdot\left(3\cdot3\right)\cdot\cdot\cdot\left(n\cdot n\right)}\)

\(\Rightarrow A=\frac{\left[1\cdot2\cdot\cdot\cdot\cdot\cdot\left(n-1\right)\right]\cdot\left[3\cdot4\cdot\cdot\cdot\cdot\cdot\left(n+1\right)\right]}{\left(2\cdot3\cdot\cdot\cdot\cdot\cdot n\right)\cdot\left(2\cdot3\cdot\cdot\cdot\cdot\cdot n\right)}\)

\(\Rightarrow A=\frac{1\cdot\left(n+1\right)}{n\cdot2}\)

\(\Rightarrow A=\frac{n+1}{2n}\)

A=(1-1/2^2)(1-1/3^2).....(1-1/n^2)

A=1(1/2^2-1/3^2-...-1/n^2)

......

xin lỗi bạn nha mình phải tắt máy rồi bạn cố gắng suy nghĩ tiếp nha

\(P=\left(-0,5-\frac{3}{5}\right):\left(-3\right)+\frac{1}{3}-\left(-\frac{1}{6}\right):\left(-2\right)\)

\(P=\left(-1,1\right):\left(-3\right)+\frac{1}{3}+\frac{1}{6}:\left(-2\right)\)

\(P=\frac{11}{30}+\frac{1}{3}+\left(-\frac{1}{12}\right)\)

\(P=\frac{37}{60}\)

\(Q=\left(\frac{2}{25}-1,008\right):\frac{4}{7}:\left[\left(3\frac{1}{4}-6\frac{5}{9}\right).2\frac{2}{17}\right]\)

\(Q=\left(-0,928\right):\frac{4}{7}:\left[\left(-\frac{119}{36}\right).2\frac{2}{17}\right]\)

\(Q=\left(-1,624\right):\left(-\frac{245}{36}\right)\)

\(Q=\frac{1044}{4375}\)