2323/202+2323/606+2323/1212+2323/2020+2323/3030+2323/4242+2323/5656+2323/7272+2323/9090. Tính nhanh
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a/
=2323 x (3434+5656)
=2323 x 9090
=21 116 070
b/
=1234 x (4244+4543)
=1234 x 8787
=10 843 159
\(\dfrac{121212}{353535}+-\dfrac{2323}{4242}\)
\(=\dfrac{12}{35}+-\dfrac{23}{42}\)
\(=-\dfrac{43}{210}\)
\(=\dfrac{12}{35}-\dfrac{23}{42}=\dfrac{72-115}{210}=\dfrac{-43}{210}\)
\(\frac{2323+1313+1414+1515+1616}{4141+2222+2323+2424+2525}\)
=\(\frac{8181}{13635}\)
\(\frac{1010+1111+1212+1313+1414+1515}{2020+2121+2222+2323+2424+2525}=\frac{10\times101+11\times101+12\times101+13\times101+14\times101+15\times101}{20\times101+21\times101+22\times101+23\times101+24\times101+25\times101}=\frac{101\times\left(10+11+12+13+14+15\right)}{101\times\left(20+21+22+23+24+25\right)}\)
\(=\frac{10+11+12+13+14+15}{20+21+22+23+24+25}=\frac{75}{135}=\frac{5}{9}\)
1010+1111+1212+1313+1414+1515= 7575
2020+2121+2222+2323+2424+2525= 13635
2323/202+2323/606+2323/1212+2323/2020+2323/3030+2323/4242+2323/5656+2323/7272+2323/9090.=
\(\frac{23\times101}{2\times101}+\frac{23\times101}{6\times101}+\frac{23\times101}{12\times101}+....+\frac{23\times101}{72\times101}+\frac{23\times101}{90\times101} \)
=\(\frac{23}{2}+\frac{23}{6}+..........+\frac{23}{72}+\frac{23}{90}\)
=\(23\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+.....+\frac{1}{9\times10}\right)\)
=\(23\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}_{ }\right)\)
=\(23\left(1-\frac{1}{10}\right)_{ }\)
=\(23\times\frac{9}{10}\)
==\(\frac{207}{10}\)
chúc học giỏi nha bn