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Đặt S = 1 x 2 + 2 x 3 + ..... + 9 x 10
3S = 1 x 2 x (3-0) + 2 x 3 x (4 - 1) + ....... + 9 x 10 x (11 - 8)
3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ......... + 9 x 10 x 11 - 8 x 9 x 10
3S = ( 1 x 2 x 3 -1 x 2 x 3) + ( 2 x 3 x4 - 2 x 3 x 4) + ..... + (8 x 9 x 10 - 8 x 9 x 10) + 9 x 10 x 11
3S = 9 x 10 x 11 = 990
S = 990 : 3 = 330
a: \(\dfrac{1}{2}+\dfrac{-3}{8}+\dfrac{5}{9}\)
\(=\dfrac{36}{72}-\dfrac{27}{72}+\dfrac{40}{72}\)
\(=\dfrac{49}{72}\)
b: \(\dfrac{13}{-30}+\dfrac{17}{45}+\dfrac{-7}{18}\)
\(=\dfrac{-13}{30}+\dfrac{17}{45}+\dfrac{-7}{18}\)
\(=\dfrac{-39+34-35}{90}=\dfrac{-40}{90}=-\dfrac{4}{9}\)
c: \(-\dfrac{5}{19}+\dfrac{7}{4}-\left(-\dfrac{2}{3}\right)+\dfrac{5}{6}\)
\(=-\dfrac{5}{19}+\dfrac{7}{4}+\dfrac{2}{3}+\dfrac{5}{6}\)
\(=\dfrac{-5}{19}+\dfrac{21+8+10}{12}\)
\(=-\dfrac{5}{19}+\dfrac{39}{12}=\dfrac{-5}{19}+\dfrac{13}{4}=\dfrac{227}{76}\)
a) =(3+11)+(4+10)+(5+9)+(6+8)+7
=14+14+14+14
=56
b)=(2+16)+(4+14)+(6+12)+(8+10)
=18+18+18+18
=72
3+4+5+6+7+8+9+10+11
= ( 3 + 11 ) + ( 4 + 10 ) + ( 5 + 19 ) + ( 6 + 8 ) + 7
= 14 + 14 + 14 + 14 + 7
= 7 x 9
= 63
Câu b tương tự bạn nhé
1!2!3!4!5!6!7!8!9!\(\Leftrightarrow\)19.28.37.46.55.64.73.82.91
\(\Leftrightarrow1^9.2^8.3^7.2^{12}.5^5.2^4.3^4.7^3.2^6.3^2\)=\(\left(2^8.2^{12}.2^4.2^6\right)\left(3^7.3^4.3^2\right)\left(5^5.7^3\right)\)
=\(2^{30}.3^{13}.5^5.7^3\)=
\(13-6-4+7-3+8-7+2=\left(13-3\right)+\left(7-7\right)+\left(8+2\right)-\left(6+4\right)=10+10-10=10\)
=(13-3)+(7-7)+(8+2)-(6+4)
=10+10-10=10