急 一到数列题[x]表示不超过实数X的最大整数,比如[3.14]=3,[0]=0,[-3.14]=-4.数列{an}满足
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急 一到数列题
[x]表示不超过实数X的最大整数,比如[3.14]=3,[0]=0,[-3.14]=-4.数列{an}满足:an=3n-2,若bn=[an/5],则b1+b2+…+b2007=?
[x]表示不超过实数X的最大整数,比如[3.14]=3,[0]=0,[-3.14]=-4.数列{an}满足:an=3n-2,若bn=[an/5],则b1+b2+…+b2007=?
![急 一到数列题[x]表示不超过实数X的最大整数,比如[3.14]=3,[0]=0,[-3.14]=-4.数列{an}满足](/uploads/image/z/18739912-40-2.jpg?t=%E6%80%A5+%E4%B8%80%E5%88%B0%E6%95%B0%E5%88%97%E9%A2%98%5Bx%5D%E8%A1%A8%E7%A4%BA%E4%B8%8D%E8%B6%85%E8%BF%87%E5%AE%9E%E6%95%B0X%E7%9A%84%E6%9C%80%E5%A4%A7%E6%95%B4%E6%95%B0%2C%E6%AF%94%E5%A6%82%5B3.14%5D%3D3%2C%5B0%5D%3D0%2C%5B-3.14%5D%3D-4.%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3)
a₁ = 1, b₁ = 0
a₂ = 4, b₂ = 0
a₃ = 7, b₃ = 1
a₄ = 10, b₄ = 2
a5 = 13, b5 = 2 b₁+ b₂+ b₃+ b₄+ b5 = 5
a6 = 16, b6 = 3
a7 = 19, b7 = 3
a8 = 21, b8 = 4
a9 = 25, b9 = 5
a10 = 28, b10 = 5 b6 + b7 + b8 + b9 + b10 = 20
a11 = 31, b10 = 6
a12 = 34, b10 = 6
a13 = 37, b10 = 7
a14 = 40, b10 = 8
a15 = 43, b10 = 8 b11 + b12 + b13+ b14 + b15 = 35
.
规律是:5 + 20 + 35 + .
项数 = 2005 ÷ 5 = 401
数列 :5 + 20 + 35 + . + (5+400×15) = (5+6000)×401÷2 = 1205005
a2006 = 3×2006 - 2 = 6016, b2006 =6016÷5 = 1203
a2007 = 3×2007 - 2 = 6019, b2006 =6016÷5 = 1203
最后答案:
b₁+ b₂+ b₃+ b₄+ b5 + .+ b2007 = 1205005 + 1203 + 1203 = 1207411
a₂ = 4, b₂ = 0
a₃ = 7, b₃ = 1
a₄ = 10, b₄ = 2
a5 = 13, b5 = 2 b₁+ b₂+ b₃+ b₄+ b5 = 5
a6 = 16, b6 = 3
a7 = 19, b7 = 3
a8 = 21, b8 = 4
a9 = 25, b9 = 5
a10 = 28, b10 = 5 b6 + b7 + b8 + b9 + b10 = 20
a11 = 31, b10 = 6
a12 = 34, b10 = 6
a13 = 37, b10 = 7
a14 = 40, b10 = 8
a15 = 43, b10 = 8 b11 + b12 + b13+ b14 + b15 = 35
.
规律是:5 + 20 + 35 + .
项数 = 2005 ÷ 5 = 401
数列 :5 + 20 + 35 + . + (5+400×15) = (5+6000)×401÷2 = 1205005
a2006 = 3×2006 - 2 = 6016, b2006 =6016÷5 = 1203
a2007 = 3×2007 - 2 = 6019, b2006 =6016÷5 = 1203
最后答案:
b₁+ b₂+ b₃+ b₄+ b5 + .+ b2007 = 1205005 + 1203 + 1203 = 1207411
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