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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 6: 2/1.3+2/3.5+2/5.7+…2/(2n+1).(2n+3)

Toán Lớp 6: 2/1.3+2/3.5+2/5.7+…2/(2n+1).(2n+3)

Comments ( 2 )

  1. 2/( 1 . 3 ) + 2/( 3 . 5 ) + 2/( 5 . 7 ) + …. + 2/( ( 2n + 1 ) . ( 2n + 3 ) )
    = 1/1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + …. + 1/( 2n + 1 ) – 1/( 2n + 3 )
    = 1 – 1/( 2n + 3 )
    = ( 2n + 3 )/( 2n + 3 ) – 1/( 2n + 3 )
    = ( 2n + 2 )/( 2n + 3 )

  2.  \frac{2}{1.3} + \frac{2}{3.5} + \frac{2}{5.7} + … + \frac{2}{(2n+1)(2n+3)}
    = 1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + … + \frac{1}{2n+1} – \frac{1}{2n+3}
    = 1 – \frac{1}{2n+3}
    = \frac{2n+2}{2n+3}
     

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222-9+11+12:2*14+14 = ? ( )