80÷(1+5%)+80÷(1+5%)²+80÷(1+5%)³+80÷(1+5%)4次方+80(1 10
80÷(1+5%)+80÷(1+5%)²+80÷(1+5%)³+80÷(1+5%)4次方+80(1+5%)5次方+1000÷(1+5%)5次方=...
80÷(1+5%)+80÷(1+5%)²+80÷(1+5%)³+80÷(1+5%)4次方+80(1+5%)5次方+1000÷(1+5%)5次方=
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3个回答
2017-01-08
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80÷(1+8%)+80÷(1+8%)^2+80÷(1+8%)^3+80÷(1+8%)^4+80÷(1+8%)^5+1000÷(1+8%)^5
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+80÷1.08^5+1000÷1.08^5
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+(80+1000)÷1.08^5
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+1080÷1.08^5
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+1000÷1.08^4
=80÷1.08+80÷1.08^2+80÷1.08^3+1000÷1.08^3
=80÷1.08+80÷1.08^2+1000÷1.08^2
=80÷1.08+1000÷1.08
=1080÷1.08
=1000
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+80÷1.08^5+1000÷1.08^5
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+(80+1000)÷1.08^5
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+1080÷1.08^5
=80÷1.08+80÷1.08^2+80÷1.08^3+80÷1.08^4+1000÷1.08^4
=80÷1.08+80÷1.08^2+80÷1.08^3+1000÷1.08^3
=80÷1.08+80÷1.08^2+1000÷1.08^2
=80÷1.08+1000÷1.08
=1080÷1.08
=1000
追问
不是= 346.358133650466吗?
追答
当然不是。
最后两个提取公因式,
(80+1000)÷1.08^5
=1080÷1.08^5
=1080÷1.08÷1.08^4
=1000÷1.08^4,
然后这一项再和前面的提取公因式,得到
80÷1.08^4+1000÷1.08^4=1000÷1.08^3,
依此类推,最终得到原式=1000
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