Tính nhanh:
D=\(\left(1-\frac{28}{10}\right)\left(1-\frac{52}{22}\right)\left(1-\frac{80}{36}\right).....\left(1-\frac{21808}{10900}\right)\)
D=18/10.30/22...........10908/10900
D=18.30........10908 / 10.22.10900
D=(2.9)(3.10).....(101.108) / (1.10)(2.11).....(100.109)
D=(2.3.......101)(9.10......108) / (1.2....100) (10.11....109)
D=101.9/109=909/109
tinh nhanh
\(\left(1-\dfrac{28}{10}\right).\left(1-\dfrac{52}{22}\right).\left(1-\dfrac{80}{36}\right)....\left(1-\dfrac{21808}{10900}\right)\)
\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
\(=\left(1-\dfrac{2.10+8}{10}\right)\left(1-\dfrac{2.22+8}{22}\right)\left(1-\dfrac{2.36+8}{36}\right)...\left(1-\dfrac{2.10900+8}{10900}\right)\)
\(=\left(1-2-\dfrac{8}{10}\right)\left(1-2-\dfrac{8}{22}\right)\left(1-2-\dfrac{8}{36}\right)...\left(1-2-\dfrac{8}{10900}\right)\)
\(=\left(-1-\dfrac{8}{1.10}\right)\left(-1-\dfrac{8}{2.11}\right)\left(-1-\dfrac{8}{3.12}\right)...\left(-1-\dfrac{8}{100.109}\right)\)
\(=\left(\dfrac{-18}{1.10}\right)\left(\dfrac{-30}{2.11}\right)\left(\dfrac{-44}{3.12}\right)...\left(\dfrac{-10908}{100.109}\right)\)
\(=\left(\dfrac{-2.9}{1.10}\right)\left(\dfrac{-3.10}{2.11}\right)\left(\dfrac{-4.11}{3.12}\right)...\left(\dfrac{-101.108}{100.109}\right)\)
\(=\dfrac{\left(-2\right)\left(-3\right)\left(-4\right)...\left(-101\right)}{1.2.3...100}.\dfrac{9.10.11...108}{10.11.12...109}\) (1)
\(=\dfrac{101}{1}.\dfrac{9}{109}=\dfrac{909}{109}\)
Do ở (1) có \(-2-\left(-101\right)+1=100\) nhân tử (số nhân tử là số chẵn) mang dấu âm nên kết quả sẽ mang dấu dương
Tính
P=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
Q=\(\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}}{\dfrac{2013}{1}+\dfrac{2014}{2}+\dfrac{2015}{3}+...+\dfrac{4023}{2011}+\dfrac{4024}{2012}-2012}\)
Bài 1 : Tính
\(A=\left(\frac{1}{3}-1\right).\left(\frac{1}{6}-1\right).\left(\frac{1}{10}-1\right).\left(\frac{1}{15}-1\right).\left(\frac{1}{21}-1\right).\left(\frac{1}{28}-1\right).\left(\frac{1}{36}-1\right)\)
HÃY CỐ GẮNG GIÚP MÌNH NHA CÁC P !!!
A = ( 1/3 - 1).( 1/6 - 1).( 1/10 - 1).( 1/15 - 1).( 1/21 - 1).( 1/28 - 1).( 1/36 - 1)
A = -2/3 . ( -5/6) . ( -9/10) . ( -14/15) . ( -20/21) . ( -27/28) . ( -35/36)
Do tích A có lẻ thừa số, mỗi thừa số đều mang dấu âm nên A mang dấu âm
A = -[ 2/3 . 5/6 . 9/10 . 14/15 . 20/21 . 27/28 . 35/36]
Đặt B = 2/3 . 5/6 . 9/10 . 14/15 . 20/21 . 27/28 . 35/36
B = 4/6 . 10/12 . 18/20 . 28/30 . 40/42 . 54/56 . 70/72
B = 1.4/2.3 . 2.5/3.4 . 3.6/4.5 . 4.7/5.6 . 5.8/6.7 . 6.9/7.8 . 7.10/8.9
B = 1.2.3.4.5.6.7/3.4.5.6.7.8.9 . 4.5.6.7.8.9.10/2.3.4.5.6.7.8
B = 2/8.9 . 9.10/2.3
B = 5/12
A = -5/12
cÓ ĐÚNG KO VẬY P NẾU ĐÚNG THÌ CHO MIK THANK Y NHA
Giúp mình với các bạn, mình đang cần gấp xin các bạn giúp mình nhé
\(\frac{1}{2}.\left(\frac{2}{9}+\frac{3}{7}-\frac{5}{27}\right);\left(\frac{-5}{28}+1,75+\frac{8}{35}\right):\left(-3\frac{9}{20}\right);\frac{1}{3}.\frac{5}{7}-\frac{7}{27}.\frac{36}{14};70,5-528:\frac{15}{2}\)
A) \(\frac{1}{2}\cdot\left(\frac{2}{9}+\frac{3}{7}-\frac{5}{27}\right)\)
\(=\frac{1}{2}\cdot\frac{1}{2}\)
\(=\frac{1}{4}\)
B) \(\left(\frac{-5}{28}+1.75+\frac{8}{35}\right):\left(-3\frac{9}{20}\right)\)
\(=\left(\frac{-5}{28}+\frac{7}{4}+\frac{8}{35}\right):\frac{-69}{20}\)
\(=\frac{14}{5}:\frac{-69}{20}\)
\(=\frac{-56}{69}\)
Tính Tổng :
\(M=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)\)
Mong mọi người giúp đỡ
2.Tính:
A=\(\left(\dfrac{1}{10}-1\right).\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right).....\left(\dfrac{1}{100}-1\right)\)
B=\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{10^2}\right)\)
C=\(\left(\dfrac{7}{9}+1\right)\left(\dfrac{7}{20}+1\right)\left(\dfrac{7}{33}+1\right)...\left(\dfrac{7}{108080}+1\right)\)
D=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{n}\right)\)với n là số tự nhiên lớn hơn 3
b)\(\left(\frac{1}{2}-1\right):\left(\frac{1}{3}-1\right):\left(\frac{1}{4}-1\right):...:\left(\frac{1}{50}-1\right)\)
Giúp mình với ạ, mình đang cần khá gấp! Cảm ơn ạ!
a, 1/2.2/3.3/4...n-1/n=1/n
b,(-1/2):..:(-49/50)=50/4=25/2
Tính:
\(M=\left(1-\frac{1}{3}\right)\left(1\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)\)
