a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1/a2n 小于3/2
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![a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1/a2n 小于3/2](/uploads/image/z/14597431-7-1.jpg?t=a1%3DA+an%2B1%3DSn%2B%28-1%29%5En%2C%E4%B8%94+an%2B2%2F3%5B%28-1%29%5En+%5D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%281%29%E6%B1%82A%E7%9A%84%E5%80%BC%2C%282%29%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan%283%29%E6%B1%82%E8%AF%811%2Fa3%2B1%2Fa4%2B.%2B1a1%3DA+an%2B1%3DSn%2B%28-1%29%5En%2C%E4%B8%94+an%2B2%2F3%5B%28-1%29%5En+%5D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%281%29%E6%B1%82A%E7%9A%84%E5%80%BC%2C%282%29%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan%283%EF%BC%89%E6%B1%82%E8%AF%811%2Fa3%2B1%2Fa4%2B.%2B1%2Fa2n+%E5%B0%8F%E4%BA%8E3%2F2)
a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1/a2n 小于3/2
a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1
a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1/a2n 小于3/2
a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1a1=A an+1=Sn+(-1)^n,且 an+2/3[(-1)^n ]是等比数列,(1)求A的值,(2)求通项公式an(3)求证1/a3+1/a4+.+1/a2n 小于3/2
1)b(n+1)=[a(n+1)-2]/[a(n+1)+1]
=[(an+2)/an-2]/[(an+2)/an+1]
=[an+2-2an]/[an+2+an]
=(2-an)/(2+2an)
=-1/2*(an-2)/(an+1)
=-1/2*bn,
所以,{bn}是首项为 (a1-2)/(a1+1)=(1-2)/(1+1)=-1/2,公比为-1/2的等比数列.
2)由1)知,bn=(-1/2)^n,
所以,Sn=(-1/2)*[1-(-1/2)^n]/(1+1/2)=-1/3*[1-(-1/2)^n]
因此,lim(n→∞)Sn=-1/3.