Toán Lớp 6: 1/19 + 9/19.29 +9/29.39 … + 9/1999.2009
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Toán Lớp 6: 1/19 + 9/19.29 +9/29.39 … + 9/1999.2009
Comments ( 2 )
1/19 + 9/(19 . 29) + 9/(29 . 39) + …. + 9/(1999 . 2009)
= 1/19 + [(10/(19 . 29) + 10/(29 . 39) + … + 10/(1999 . 2009)) . 9/10]
= 1/19 + [(1/19 – 1/29 + 1/29 – 1/39 + … + 1/1999 – 1/2009) . 9/10]
= 1/19 + [(1/19 – 1/2009) . 9/10]
= 1/19 + [1990/38171 . 9/10]
= 1/19 + 1791/38171
= 200/2009
1/19 + frac{9}{19 . 29} + frac{9}{29 . 39} + …. + frac{9}{1999 . 2009}
=1/19 + (frac{9}{19 . 29} + frac{9}{29 . 39} + …. + frac{9}{1999 . 2009})
=1/19 + 9/10(frac{10}{19.29} + frac{10}{29.39} + … + frac{10}{1999.2009})
=1/19 + 9/10(1/19 – 1/29 + 1/29 – 1/39 + …. + 1/1999 – 1/2009)
=1/19 + 9/10 (1/19 – 1/2009)
=1/19 + 9/10 . 1990/38171
=1/19 + 1791/38171
=200/2009