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Câu hỏi của Nguyễn Văn Duyệt - Toán lớp 5 - Học toán với OnlineMath
Em tham khảo nhé!
T = 3/4 x 8/9 x 15/16 x ... x 575/576 x 624/625
T = (1x3/1x4) x (2x4/3x3) x (3x5/4x4) x ... x (23x25/24x24) x (24x26/25x25)
T = [1 x 2/3 x 3/4 x 4/5 x ... x 23/24 x 24/25] x [3/5 x 4/3 x 5/4 x 6/5 x ... x 25/24 x 26/25]
T = 2/25 x 26/5
T = 52/125
\(B=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}\)
\(B=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{9999}{100^2}\)
\(B=\frac{3.8.15...9999}{2^2.3^2.4^2...100^2}\)
\(B=\frac{1.3.2.4.3.5...99.101}{2.2.3.3.4.4...100.100}\)
\(B=\frac{\left(1.2.3...99\right).\left(3.4.5...101\right)}{\left(2.3.4...100\right).\left(2.3.4...100\right)}\)
\(B=\frac{1.101}{100.2}\)
\(B=\frac{101}{200}\)
\(C=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right).\left(1+\frac{1}{100}\right)\)
\(C=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{100}{99}.\frac{101}{100}\)
\(C=\frac{3.4.5...100.101}{2.3.4...99.100}\)
\(C=\frac{101}{2}\)
Dấu . là dâú x nha
\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x...x\left(1-\frac{1}{576}\right)x\left(1-\frac{1}{625}\right)\)
\(=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x...x\frac{575}{576}x\frac{624}{625}=\frac{1x3}{1x4}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x...x\frac{23x25}{24x24}x\frac{24x26}{25x25}\)
\(=\left(\frac{1}{1}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{23}{24}x\frac{24}{25}=\frac{1x2x3x4x...x23x24}{1x3x4x5x...x24x25}=\frac{2}{25}\right)\left(\frac{3}{5}x\frac{4}{3}x\frac{5}{4}x\frac{6}{5}x...x\frac{25}{24}x\frac{26}{25}=\frac{3x4x5x6x...x25x26}{5x3x4x5x...x24x25}=\frac{26}{5}\right)\)
\(\frac{2}{25}x\frac{26}{5}=\frac{52}{50}=\frac{26}{25}\)
A = \(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+..+9\right)}{1\times2+2\times3+3\times4+...+19\times20}\)
\(=\frac{\frac{1\times\left(1+1\right)}{2}+\frac{2\times\left(2+1\right)}{2}+\frac{3\times\left(3+1\right)}{2}...+\frac{9\times\left(9+1\right)}{2}}{1\times2+2\times3+3\times4+...+19\times20}\)
\(=\frac{\frac{1\times2}{2}+\frac{2\times3}{2}+\frac{3\times4}{2}+...+\frac{9\times10}{2}}{1\times2+2\times3+3\times4+...+9\times10}\)
\(=\frac{\frac{1}{2}\times\left(1\times2+2\times3+3\times4+...+9\times10\right)}{1\times2+2\times3+3\times4+...+9\times10}=\frac{\frac{1}{2}}{1}=\frac{1}{2}\)
Sửa đề : \(T=\left[1-\frac{1}{4}\right]\times\left[1-\frac{1}{9}\right]\times\left[1-\frac{1}{16}\right]\times...\times\left[1-\frac{1}{576}\right]\times\left[1-\frac{1}{625}\right]\)
\(T=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{575}{576}\cdot\frac{624}{625}\)
\(T=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{23\cdot25}{24\cdot24}\cdot\frac{24\cdot26}{25\cdot25}\)
\(T=\frac{1\cdot2\cdot3\cdot....\cdot23\cdot24}{2\cdot3\cdot4\cdot....\cdot24\cdot25}\cdot\frac{3\cdot4\cdot5\cdot...\cdot25\cdot26}{2\cdot3\cdot4\cdot...\cdot24\cdot25}\)
Đến đây dễ rồi nhé bạn :v
\(T=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{157}\right)\times\left(1-\frac{1}{625}\right)\)
\(T=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{156}{157}\times\frac{624}{625}\)
\(T=\frac{3\times2\times4\times3\times5\times...\times23\times25\times24\times26}{2\times2\times3\times3\times4\times4\times...\times24\times24\times25\times25}\)
\(T=\frac{1\times26}{2\times25}=\frac{26}{50}=\frac{13}{25}\)