b)C=1+4(99+3)49/2+97.99.101.103/8
Tinh a)B=(1+4.3+4.5+..+4.99)(1.3.5+3.5.7+...+97.99.100)
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13 tháng 10 2023
a) 9 + 99 + 999 + ... + 999999
= (10 - 1) + (100 - 1) + (1000 - 1) + ... + (1000000 - 1)
= (101 + 102 + 103 + ... + 106) - (1.6)
= 1111110 - 6 = 1111104
b) 1 + 11 + 111 + ... + 1111111
= 1 + (101 + 1) + (102 + 101 + 1) + ... + (106 + 105 + 104 + 103 + 102 + 101 + 1)
= 101 . 6 + 102 . 5 + 103 . 4 + ... + 106. 1) + (1 + 1.6)
= 60 + 500 + 4000 + ... + 1000000 + 7
= 1234560 + 7 = 1234567
c) C = 1.2 + 2.3 + 3.4 + 4.5 + ... + 98.99
3C = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 98.99.3
3C = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 98.99.(100 - 97)
3C = 1.2.3 + 2.3.4 - 2.3.1 + 3.4.5 - 3.4.2 +...+ 98.99.100 - 98.99.97
3C = 98.99.100
C = \(\dfrac{98.99.100}{3}\) = 323400
d) D = 1.3.5 + 3.5.7 + 5.7.9 + ... + 95.97.99
8D = 1.3.5.8 + 3.5.7.8 + 5.7.9.8 + ... + 95.97.99.8
8D = 1.3.5.(7 + 1) + 3.5.7.(9 - 1) + 5.7.9.(11 - 3) + ... + 95.97.99.(101 - 93)
8D = 1.3.5.7 + 1.3.5.1 + 3.5.7.9 - 3.5.7.1 + 5.7.9.11 - 5.7.9.3 + ... + 95.97.99.101 - 95.97.99.93
8D = 1.3.5.1 + 95.97.99.101
D = \(\dfrac{1.3.5.1+95.97.99.101}{8}=15517600\)
15 tháng 4 2023
a: \(=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+...+\dfrac{1}{18\cdot19}-\dfrac{1}{19\cdot20}\)
=1/2-1/380
=179/380
b: \(=\dfrac{1}{1\cdot3}-\dfrac{1}{3\cdot5}+\dfrac{1}{3\cdot5}-\dfrac{1}{5\cdot7}+...+\dfrac{1}{21\cdot23}-\dfrac{1}{23\cdot25}\)
\(=\dfrac{1}{3}-\dfrac{1}{575}=\dfrac{572}{1725}\)
c: \(=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}+\dfrac{1}{20}-\dfrac{1}{20}-\dfrac{1}{21}\)
=1-1/21
=20/21
d: \(=\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)\cdot...\cdot\left(1-\dfrac{1}{121}\right)\)
\(=\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{10}{11}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{12}{11}\)
\(=\dfrac{2}{11}\cdot\dfrac{12}{2}=\dfrac{12}{11}\)
22 tháng 6 2022
a: \(\dfrac{4\cdot5+4\cdot11}{8\cdot7+4\cdot3}=\dfrac{20+44}{56+12}=\dfrac{64}{68}=\dfrac{16}{17}=\dfrac{11088}{11781}\)
\(\dfrac{-15\cdot8+10\cdot7}{5\cdot6+20\cdot3}=\dfrac{-120+70}{30+60}=\dfrac{-50}{90}=\dfrac{-5}{9}=\dfrac{-6545}{11781}\)
\(\dfrac{2^4\cdot5^2\cdot7}{2^3\cdot5\cdot7^2\cdot11}=\dfrac{2\cdot5}{7\cdot11}=\dfrac{10}{77}=\dfrac{1530}{11781}\)