rút gọn phân số:
A=1212+1313+1414+...+2020/1717+1818+1919+...+3131
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A = \(\dfrac{1414+1515+1616+1717+1818+1919}{2020+2121+2022+2323+2424+2525}\)
A = \(\dfrac{101\times\left(14+15+16+17+18+19\right)}{101\times\left(20+21+22+23+24+25\right)}\)
A = \(\dfrac{99}{135}\)
A = \(\dfrac{11}{15}\)
=\(\frac{14x101+15x101+16x101+18x101+19x101}{20x101+21x101+22x101+23x101+24x101+25x101}\)
=\(\frac{101x\left(14+15+16+17+18+19\right)}{101x\left(20+21+22+23+24+25\right)}\)
=\(\frac{14+15+16+17+18}{20+21+22+23+24+25}=\frac{99}{135}=\frac{11}{15}\)
\(S=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{2022}\right)\left(1-\dfrac{1}{2023}\right)\)
\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}....\dfrac{2022}{2023}\)
\(=\dfrac{1.2.3....2022}{2.3.4....2023}\)
\(=\dfrac{1}{2023}\)
1414+1515+1616+1717+1818+1919/2020+2121+2222+2323+2424+2525
=14.101+15.101+16.101+17.101+18.101+19.101/20.101+21.101+22.101+23.101+24.101+25.101
=14+15+16+17+18+19/20+21+22+23+24+25
=99/135
=11/15
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