bài1: tính nhanh 1/1000+13/1000+25/1000+37/1000+49/1000+……..+85/1000+97/1000 1/2+1/6+1/12+1/20+1/30+1/42+…….+1/90 1/3

1 bình luận về “bài1: tính nhanh 1/1000+13/1000+25/1000+37/1000+49/1000+……..+85/1000+97/1000 1/2+1/6+1/12+1/20+1/30+1/42+…….+1/90 1/3”

1. Giải đáp:

    

   Lời giải và giải thích chi tiết:

   Bài 1:
   1/1000+13/1000+25/1000+37/1000+49/1000+…+85/1000+97/1000
   = (1+13+25+37+49+…+85+97)/1000
   = (1+3+5+7+9+…+43+49)/100
   = [(1+49)+(3+47)+(5+45)+…+(43+7)]/100
   = [50+50+50+…+50]/100
   = 25

   1/2+1/6+1/12+1/20+1/30+1/42+…+1/90
   = (1/1-1/2) + (1/2-1/3) + (1/3-1/4) + … + (1/9-1/10)
   = 1 – 1/10
   = 9/10

   1/3+1/9+1/27+1/81+…+1/59049
   = (1-1/3)/(1-1/3^11)
   = 2/3 × (1-1/3^10)
   = 2/3 × (59048/59049)
   = 118096/177147

   Bài 2:
   1/1×2+1/2×3+1/3×4+1/4×5+…+1/98×99+1/99×100
   = [(1/1)-(1/2)] + [(1/2)-(1/3)] + [(1/3)-(1/4)] + … + [(1/98)-(1/99)] + [(1/99)-(1/100)]
   = 1 – 1/100
   = 99/100

    

   Trả lời