已知数列{an}满足:a1=1,a2=2,且 an+2=(2+cosnπ)(an-1)+3,n∈N
已知数列{an}满足:a1=1,a2=2,且an+2=(2+cosnπ)(an-1)+3,n∈N+求通项公式an...
已知数列{an}满足:a1=1,a2=2,且 an+2=(2+cosnπ)(an-1)+3,n∈N+
求通项公式an 展开
求通项公式an 展开
2个回答
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a(n+2)=(2+cosnπ)(an -1)+3
if n is odd
a(n+2)=(2+cosnπ)(an -1)+3
a(n+2)=(2-1)(an -1)+3
= an +2
a(n+2) -an = 2
an - a1= n-1
an = n
if n is even
a(n+2)=(2+cosnπ)(an -1)+3
= 3(an -1)+3
a(n+2) = 3an
an/a2 = 3^[(n-2)/2]
an = 2. 3^[(n-2)/2]
ie
an = n ,if n is odd
=2. 3^[(n-2)/2] , if n is even
if n is odd
a(n+2)=(2+cosnπ)(an -1)+3
a(n+2)=(2-1)(an -1)+3
= an +2
a(n+2) -an = 2
an - a1= n-1
an = n
if n is even
a(n+2)=(2+cosnπ)(an -1)+3
= 3(an -1)+3
a(n+2) = 3an
an/a2 = 3^[(n-2)/2]
an = 2. 3^[(n-2)/2]
ie
an = n ,if n is odd
=2. 3^[(n-2)/2] , if n is even
追问
翻译为我看的懂得好么
追答
a(n+2)=(2+cosnπ)(an -1)+3
若 n 是奇数
a(n+2)=(2+cosnπ)(an -1)+3
a(n+2)=(2-1)(an -1)+3
= an +2
a(n+2) -an = 2
an - a1= n-1
an = n
若 n 是偶数
a(n+2)=(2+cosnπ)(an -1)+3
= 3(an -1)+3
a(n+2) = 3an
an/a2 = 3^[(n-2)/2]
an = 2. 3^[(n-2)/2]
ie
an = n ,若 n 是奇数
=2. 3^[(n-2)/2] ,若 n 是偶数
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