2道简单求数列通项题.1.a1=1 a(n+1)=an+2^(n-1) 求an2.a1=4 a(n+1)=an+5^n 求an
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2道简单求数列通项题.1.a1=1 a(n+1)=an+2^(n-1) 求an2.a1=4 a(n+1)=an+5^n 求an
2道简单求数列通项题.
1.
a1=1 a(n+1)=an+2^(n-1) 求an
2.
a1=4 a(n+1)=an+5^n 求an
2道简单求数列通项题.1.a1=1 a(n+1)=an+2^(n-1) 求an2.a1=4 a(n+1)=an+5^n 求an
1.a(n+1)-an=2^(n-1)
an-a(n-1)=2^(n-2)
......
a2-a1=2^0 (n>1)
叠加得 an-a1=2^0+2^1+...+2^(n-2)=[2^0-2^(n-1)]/(1-2)=2^(n-1)-1
an=2^(n-1) 当n=1时也符合 所以an=2^(n-1)
2.方法同上 答案:an=(5^n+11)/4