a)2+2/3+2/9+2/27+….+2/729+2/2187 b)1/1×3+1/3×5+1/5×7+…+1/17×19+1/19×21

1 bình luận về “a)2+2/3+2/9+2/27+….+2/729+2/2187 b)1/1×3+1/3×5+1/5×7+…+1/17×19+1/19×21”

1. Giải đáp:

   a)A=6560/2187

   b)B=10/21 

   Lời giải và giải thích chi tiết:

   a)
   Đặt:
   A=2+2/3+2/9+2/27+….+2/729+2/2187
   =2+2/3+2/3^2+2/3^3+…+2/3^6+2/3^7
   =>3A=6+2+2/3+2/3^2+…+2/3^5+2/3^6
   =>3A-A=(6+2+2/3+2/3^2+…+2/3^5+2/3^6)-(2+2/3+2/3^2+2/3^3+…+2/3^6+2/3^7)
   =>2A=6-2/{3^7}={6.3^7-2}/{3^7}
   =>A={6.3^7-2}/{2.3^7}
   =>A=6560/2187

   b)
   Đặt:
   B=1/{1.3}+1/{3.5}+1/{5.7}+…+1/{17.19}+1/{19.21}
   =>2B=2/{1.3}+2/{3.5}+2/{5.7}+…+2/{17.19}+2/{19.21}
   =1-1/3+1/3-1/5+1/5-1/7+…+1/17-1/19+1/19-1/21
   =1-1/21
   =20/21
   =>B=10/21 

   Trả lời