高三極限題目
試求有規律的極限題目:1+4/5+7/5^2+10/5^3+...+3n-2/5^n-1+....=?
答案:35/16
不知道該怎麼下手,求算式,謝謝
回答 (2)
Sol
1,4,7,10,…=>等差
1,5,5^2,5^3,….=>等比
A=1+4/5+7/5^2+10/5^3+...+(3n-2)/5^(n-1)+....
A/5=1/5+4/5^2+7/5^3+...+(3n-5)/5^(n-1)+....
-------------------------------------------------------------
4A/5=1+3/5+3/5^2+3/5^3+….+3/5^(n-1)+….
=1+(3/5)/(1-1/5)
=1+3/(5-1)
=7/4
A=(5/4)*(7/4)=35/16
收錄日期: 2021-04-30 18:31:59
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