数列{an}满足an=2+1/5An-1(n>1)且a1=5,则an=?An-1 n-1是下角标、
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数列{an}满足an=2+1/5An-1(n>1)且a1=5,则an=?An-1 n-1是下角标、
数列{an}满足an=2+1/5An-1(n>1)且a1=5,则an=?
An-1 n-1是下角标、
数列{an}满足an=2+1/5An-1(n>1)且a1=5,则an=?An-1 n-1是下角标、
是(1/5)·a(n-1)吗?
只要把它化成 an + m =(1/5)[a(n-1)+m]的形式就行
an + m =(1/5)[a(n-1)+m]
an + m =(1/5)a(n-1)+ m/5
an=(1/5)a(n-1) - 4m/5
∴ - 4m/5 =2
m= -5/2
∴an - 5/2 =(1/5)[a(n-1) - 5/2]
∴数列{an - 5/2}是以a1 - 5/2=5/2为首项,1/5为公比的等比数列
∴an- 5/2=(5/2)·(1/5)^(n-1)=1/[2·5^(n-2)]
an=1/[2·5^(n-2)] + 5/2=[1+5^(n-1)]/[2·5^(n-2)]
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