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

Toán Lớp 6: Tính các tổng sau. a) 1 + 2 + 3 + 4 +-+ n b) 2 + 4 + 6 + 8 +…+ 2.n c) 1 + 3 + 5 + 7+…+ (2.n +1)

Toán Lớp 6: Tính các tổng sau.
a) 1 + 2 + 3 + 4 +….+ n b) 2 + 4 + 6 + 8 +…+ 2.n
c) 1 + 3 + 5 + 7+…+ (2.n +1) d) 1 + 4 + 7 + 10 +..+ 2005
e) 2 + 5 + 8 +…+ 2006 f) 1 + 5 + 9 +…+ 2001

Comments ( 1 )

  1. a) 1 + 2+3+4 + … + n
    = \frac{(1+n)[(n-1):1+1]}{2}
    = \frac{(n+1)n}{2}
     b) 2 + 4 + 6 + … + 2n
    = \frac{(2+2n)[(2n – 2):2 + 1]}{2}
    = \frac{(2n+2)n}{2}
    = n(n+1)
     c)  1 + 3 + 5 + 7 + … + (2n + 1)
    = \frac{(1 + 2n + 1)[(2n + 1 – 1) : 2 + 1]}{2}
    = \frac{(2n+2)(n+1)}{2}
    = (n+1)^2
     d) 1 + 4 + 7 + 10 + … + 2005
    = \frac{(1 + 2005)[(2005-1) : 3 + 1]}{2}
    = \frac{2006 . 669}{2}
    = 671007
     e) 2 + 5 + 8 + … + 2006
    =\frac{(2+2006)[(2006-2):3+1]}{2}
    = \frac{2008.669}{2}
    = 671676
     d) 1 + 5 + 9 + … + 2001
    = \frac{(1+2001)[(2001 – 1) : 4 + 1]}{2}
    = \frac{2002.501}{2}
    = 501501
     

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