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ai mak chẳng bt đó lak dấu nhân bn lần sau khỏi phải gt mất công
Tham khảo:
A=1.2+2.3+3.4+...+2013.2014
3A = 1.2.3 + 2.3.3 + 3.4.3 +...+ 2013.2014.3
Mà: 1.2.3 = 1.2.3
2.3.3 = 2.3.4 - 2.3.1
3.4.3 = 3.4.5 - 3.4.2
2012.2013.3 = 2012.2013.2014 - 2012.2013.2011
2013.2014.3 = 2013.2014.2015 - 2013.2014.2012
=> 3S = 2013.2014.2015
=> A = 2013.2014.2015 / 3 = 2723058910
3A= 1.2.3+2.3.3+3.4.3+...........+2010.2011.3
3A=1.2.3+2.3.(4-1)+3.4.(5-2)+.........+2010.2011.(2012-2009)
=>3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.....+2010.2011.2012-2009.2010.2011
=>3A=2010.2011.2012
=>3A=3.670.2011.2012
=>A=670.2011.2012
=>A= .......lấy máy tính mà tính
a) 2021 + 2022 + 2023 + 2024 + 2025 + 2026 + 2027 + 2028 + 2029
= (2021 + 2029) + (2022 + 2028) + (2023 + 2027) + (2024 + 2026) + 2025
= 4050 + 4050 + 4050 + 4050 + 2025
= 4050.4 + 2025
= 16 200 + 2025
= 18 225
b)
30.40.50.60 = 3.10.4.10.5.10.6.10 = 3.4.5.6.10000 = 3.20.6.10000 = 3.2.6.10.10000 = 36.100000 = 3600000
E = 1.2+2.3+3.4+......+99.100
Gấp E lên 3 lần ta có:
E . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
E . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
E . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 E . 3 = 99.100.101
E = 99.100.101 : 3
E = 33.100.101
E = 333 300
k mik nha
E = 1.2 + 2.3 + 3.4 + ... + 99.100
=> 3E = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3
=> 3E = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) +...+ 99.100.(101-98)
=> 3E = 1.2.3 - 0 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
=> 3E = 99.100.101
=> E = 333300
\(S=\dfrac{2^2}{1.2}+\dfrac{2^2}{2.3}+\dfrac{2^2}{3.4}+...+\dfrac{2^2}{2022.2023}\)
\(S=2^2.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2022.2023}\right)\)
\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\right)\)
\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2023}\right)\)
\(S=2^2.\dfrac{2022}{2023}\)
\(S=\dfrac{2^2.2022}{2023}=\dfrac{8088}{2023}\)
Tính nhanh: A= \(\dfrac{2022}{1.2}+\dfrac{2022}{2.3}+\dfrac{2022}{3.4}+...+\dfrac{2022}{2021.2022}\)
A=2022(1/1-1/2+1/2-1/3+...+1/2021-1/2022)
=2022(1/1-1/2022)
=2022.2021/2022
ket qua tu tinh nha
A = \(\dfrac{2022}{1.2}+\dfrac{2022}{2.3}+\dfrac{2022}{3.4}+...+\dfrac{2022}{2021.2022}\)
= \(\dfrac{2022}{1}-\dfrac{2022}{2}+\dfrac{2022}{2}-\dfrac{2022}{3}+\dfrac{2022}{3}-\dfrac{2022}{4}+...+\dfrac{2022}{2021}-\dfrac{2022}{2022}\)
= \(\dfrac{2022}{1}-\dfrac{2022}{2022}\)
= \(2021\)
Chúc bạn học tốt!! ^^
Đặt B = 1.2 + 2.3 + 3.4 + ... + 2022.2023
⇒ 3B = 1.2.3 + 2.3.3 + 3.4.3. + ... + 2022.2023.3
= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 2022.2023.(2024 - 2021)
= 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 + ... - 2021.2022.2023 + 2022.2023.2024
= 2022.2023.2024
⇒ B = 2022.2023.2024 : 3 = 2759728048
⇒ A = 2759728048/(2022 + 2023 + 2024)
= 1364176/3
Đặt B = 1.2 + 2.3 + 3.4 + ... + 2022.2023
⇒ 3B = 1.2.3 + 2.3.3 + 3.4.3. + ... + 2022.2023.3
= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 2022.2023.(2024 - 2021)
= 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 + ... - 2021.2022.2023 + 2022.2023.2024
= 2022.2023.2024
⇒ B = 2022.2023.2024 : 3 = 2759728048
⇒ A = 2759728048/(2022 + 2023 + 2024)
= 1364176/3