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  • 已知數(shù)列{an}滿足:a1=1,a2=2,且 an+2=(2+cosnπ)(an-1)+3,n∈N+

    已知數(shù)列{an}滿足:a1=1,a2=2,且 an+2=(2+cosnπ)(an-1)+3,n∈N+
    求通項(xiàng)公式an
    數(shù)學(xué)人氣:984 ℃時(shí)間:2020-06-14 22:34:38
    優(yōu)質(zhì)解答
    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翻譯為我看的懂得好么a(n+2)=(2+cosnπ)(an -1)+3
    若 n 是奇數(shù)
    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 是偶數(shù)
    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 是奇數(shù)
    =2. 3^[(n-2)/2] ,若 n 是偶數(shù)
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