周期性函数递推设数列{an}满足a1=a2=1,a3=2,且对任意正整数n都有an*an+1*an+2≠1,又an*an+1*an+2*an+3=an+an+1+an+2+an+3,求a1+a2+…a100
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![周期性函数递推设数列{an}满足a1=a2=1,a3=2,且对任意正整数n都有an*an+1*an+2≠1,又an*an+1*an+2*an+3=an+an+1+an+2+an+3,求a1+a2+…a100](/uploads/image/z/12381307-43-7.jpg?t=%E5%91%A8%E6%9C%9F%E6%80%A7%E5%87%BD%E6%95%B0%E9%80%92%E6%8E%A8%E8%AE%BE%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E6%BB%A1%E8%B6%B3a1%3Da2%3D1%2Ca3%3D2%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E6%AD%A3%E6%95%B4%E6%95%B0n%E9%83%BD%E6%9C%89an%2Aan%2B1%2Aan%2B2%E2%89%A01%2C%E5%8F%88an%2Aan%2B1%2Aan%2B2%2Aan%2B3%3Dan%2Ban%2B1%2Ban%2B2%2Ban%2B3%2C%E6%B1%82a1%2Ba2%2B%E2%80%A6a100)
周期性函数递推设数列{an}满足a1=a2=1,a3=2,且对任意正整数n都有an*an+1*an+2≠1,又an*an+1*an+2*an+3=an+an+1+an+2+an+3,求a1+a2+…a100
周期性函数递推
设数列{an}满足a1=a2=1,a3=2,且对任意正整数n都有an*an+1*an+2≠1,又an*an+1*an+2*an+3=an+an+1+an+2+an+3,求a1+a2+…a100
周期性函数递推设数列{an}满足a1=a2=1,a3=2,且对任意正整数n都有an*an+1*an+2≠1,又an*an+1*an+2*an+3=an+an+1+an+2+an+3,求a1+a2+…a100
an*a(n+1)*a(n+2)*a(n+3)=an+a(n+1)+a(n+2)+a(n+3)
a(n+1)*a(n+2)*a(n+3)*a(n+4)=a(n+1)+a(n+2)+a(n+3)+a(n+4)
a(n+4)/an=[an+a(n+1)+a(n+2)+a(n+3)]/[an+a(n+1)+a(n+2)+a(n+3)]
[a(n+4)-an][a(n+1)+a(n+2)+a(n+3)]=0
∵a1+a2+a3=4
∴a(n+1)+a(n+2)+a(n+3)≠0
a(n+4)=an
1*1*2*a4=1+1+2+a4
a4=4
a5=a1,a6=a2,a7=a3a8=a4,...
a1+a2+…a100=25*(a1+a2+a3+a4)=200
而无法
周期性函数递推设数列{an}满足a1=a2=1,a3=2,且对任意正整数n都有an*an+1*an+2≠1,又an*an+1*an+2*an+3=an+an+1+an+2+an+3,求a1+a2+…a100
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