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 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 :
\(\left(1-\frac{1}{21}\right)\times\left(1-\frac{1}{28}\right)\times\left(1-\frac{1}{36}\right)\times....\times\)\(\left(1-\frac{1}{1326}\right)\)
\(\left(\frac{1}{3}-1\right)\times\left(\frac{1}{6}-1\right)\times\left(\frac{1}{10}-1\right)\times\left(\frac{1}{15}-1\right)\times...\times\left(\frac{1}{1225}-1\right)\times\left(\frac{1}{1275}-1\right)\)=?
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
\(\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{10}\right)\times\left(1-\frac{1}{15}\right)\times...\times\left(1-\frac{1}{780}\right)\)
(1+-1/3)x(1+-1/6)x.....x(1+-1/780)=0+0+0+....+0=0
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)
Tìm tích:
1.\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\left(\frac{1}{4}+1\right)\times...\times\left(\frac{1}{999}+1\right)\)
2.\(\left(\frac{1}{2}-1\right)\times\left(\frac{1}{3}-1\right)\times\left(\frac{1}{4}-1\right)\times...\times\left(\frac{1}{1000}-1\right)\)
3.\(\frac{3}{2^2}\times\frac{8}{3^2}\times\frac{15}{4^2}\times...\times\frac{99}{10^2}\)
biết làm bài 1 thôi
\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\cdot\cdot\cdot\times\left(\frac{1}{999}+1\right)\)
= \(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdot\cdot\cdot\times\frac{1000}{999}\)
lượt bỏ đi còn :
\(\frac{1000}{2}=500\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{20}\right)\)