Tính :
\(\left(1-\frac{1}{21}\right)\times\left(1-\frac{1}{28}\right)\times\left(1-\frac{1}{36}\right)\times....\times\)\(\left(1-\frac{1}{1326}\right)\)
tính các tích sau: \(A=\left(1-\frac{1}{21}\right)\times\left(1-\frac{1}{28}\right)\times\left(1-\frac{1}{36}\right)\times....\times\left(1-\frac{1}{1326}\right)\)
\(A=\frac{20}{21}\cdot\frac{27}{28}\cdot\frac{35}{36}\cdot...\cdot\frac{1325}{1326}\)
\(=\frac{40}{42}\cdot\frac{54}{56}\cdot\frac{70}{72}\cdot...\cdot\frac{2650}{2652}\)
\(=\frac{5\cdot8}{6\cdot7}\cdot\frac{6\cdot9}{7\cdot8}\cdot\frac{7\cdot10}{8\cdot9}\cdot...\cdot\frac{50\cdot53}{51\cdot52}\)
\(=\frac{5\cdot53}{7\cdot51}=\frac{265}{357}\)
Tính\(\left(1-\frac{1}{15}\right)\times\left(1-\frac{1}{21}\right)\times\left(1-\frac{1}{28}\right)\times......\times\left(1-\frac{1}{20}\right)\)
Tính\(\left(1-\frac{1}{15}\right)\times\left(1-\frac{1}{21}\right)\times\left(1-\frac{1}{28}\right)\times.....\times\left(1-\frac{1}{20}\right)\)
Tính nhanh:
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times.......\times\left(1-\frac{1}{2003}\right)\times\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times....\times\frac{2003}{2004}\)
\(=\frac{1\times2\times3\times...\times2003}{2\times3\times4\times...\times2014}\)
\(=\frac{1}{2014}\)
Tính : \(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{576}\right)\times\left(1-\frac{1}{624}\right)\)
\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{625}\right)\)
\(=\frac{3}{4}\times\frac{8}{9}\times...\times\frac{623}{624}\)
\(=\frac{1\times3}{2\times2}\times\frac{2\times4}{3\times3}\times...\times\frac{24\times26}{25\times25}\)
\(=\frac{1\times3\times2\times4\times...\times24\times26}{2\times2\times3\times3\times...\times25\times25}\)
Từ đây mình viết nhân là chấm nha mong bạn thông cảm :
\(=\frac{\left(1\cdot2\cdot3\cdot...\cdot24\right)\cdot\left(3\cdot4\cdot5\cdot...\cdot26\right)}{\left(2\cdot3\cdot4\cdot...\cdot25\right)\cdot\left(2\cdot3\cdot4\cdot...\cdot25\right)}\)
\(=\frac{1\cdot26}{25\cdot2}\)
\(=\frac{26}{50}=\frac{13}{25}\)
k tớ nha
Tính nhanh:
P = \(\frac{1}{5x8}+\frac{1}{8x11}+\frac{1}{11x14}+..........+\frac{1}{602x605}\)
Q = \(\frac{4}{3x7}+\frac{5}{7x12}+\frac{1}{12x13}+\frac{7}{13x20}+\frac{3}{20x23}\)
R = \(\left(1-\frac{1}{15}\right)\times\left(1-\frac{1}{21}\right)\times\left(1-\frac{1}{28}\right)\times........\times\left(1-\frac{1}{210}\right)\)
\(P=\frac{1}{5x8}+\frac{1}{8x11}+.....+\frac{1}{602x605}\)
\(\Rightarrow3P=\frac{3}{5x8}+\frac{3}{8x11}+......+\frac{3}{602x605}\)
\(\Rightarrow3P=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-.....+\frac{1}{602}-\frac{1}{605}\)
\(\Rightarrow3P=\frac{1}{5}-\frac{1}{605}\)
\(\Rightarrow3P=\frac{24}{121}\)
\(\Rightarrow P=\frac{24}{121}:3\)
\(\Rightarrow P=\frac{8}{121}\)
\(Q=\frac{4}{3x7}+\frac{5}{7x12}+\frac{1}{12x13}+\frac{7}{13x20}+\frac{3}{20x23}\)
\(Q=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{23}\)
\(Q=\frac{1}{3}-\frac{1}{23}\)
\(Q=\frac{20}{69}\)
câu 1 = 1/5 -1/8+1/8 -1/11+1/11-1/14+.....+1/602-1/605
bây giờ cậu xoá các phân số gống nhau mà có phép cộng như 1/8+1/8 là xoá tương tự như vậy xoá các phân số bằng dấu gạch các phân số như / thế đó nhé
là xoá hết còn phân số 1/5-1/605 mà trừ là theo kiểu tìm x nhé
Tính P = \(\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times\left(1+\frac{1}{4\times6}\right)\times...\times\left(1+\frac{1}{2009\times2011}\right)\)
(1+\(\frac{1}{3}\)) x (1+\(\frac{1}{2x4}\)) x(1+\(\frac{1}{3x5}\))x(1+\(\frac{1}{4x6}\)) x .....x (1+ \(\frac{1}{2009x2011}\))
= \(\frac{2}{1x3}\)x \(\frac{2}{2x4}\)x \(\frac{2}{3x5}\)x \(\frac{2}{4x6}\)x....x \(\frac{2}{2009x2011}\)
= ..................
đến đây tự làm nhé
tính các tích sau
\(a=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{9999}{10000}\)
\(b=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{10000}\right)\)
\(c=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(d=\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times...\times\left(1+\frac{1}{99\times100}\right)\)
\(d=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).........\left(1+\frac{1}{99.101}\right)\)
\(=\frac{4}{3}.\frac{9}{2.4}.............\frac{10000}{99.101}\)
\(=\frac{2.2}{3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}............\frac{100.100}{99.101}\)
\(=\frac{2.3.4..........100}{2.3.4............99}.\frac{2.3.4...........100}{3.4...........101}\)
\(=100.\frac{2}{101}\)\(=\frac{200}{101}\)
\(C=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{1993}{1994}\)
\(=\frac{1\times2\times3\times...\times1993}{2\times3\times4\times...\times1994}\)
\(=\frac{1}{1994}\) (Giản ước còn lại như này)
Tính giá trị biểu thức: A=\(\frac{\left(1+17\right)\times\left(1+\frac{17}{2}\right)\times\left(1+\frac{17}{3}\right)....\left(1+\frac{17}{19}\right)}{\left(1+19\right)\times\left(1+\frac{19}{2}\right)\times\left(1+\frac{19}{3}\right)....\left(1+\frac{19}{17}\right)}\)