已知数列{an},{bn}与函数f(x),g(x),x∈R满足条件:b1=b,an=f(bn)=g(b(n+1))(n∈N*)若f(x)=tx+1(t≠0,t≠2),g(x)=2x,f(b)≠g(b),且lim(an)(n→∞)存在,求t的取值范围,并求lim(an)(n→∞)(用t表示).
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![已知数列{an},{bn}与函数f(x),g(x),x∈R满足条件:b1=b,an=f(bn)=g(b(n+1))(n∈N*)若f(x)=tx+1(t≠0,t≠2),g(x)=2x,f(b)≠g(b),且lim(an)(n→∞)存在,求t的取值范围,并求lim(an)(n→∞)(用t表示).](/uploads/image/z/5316656-32-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%2C%7Bbn%7D%E4%B8%8E%E5%87%BD%E6%95%B0f%28x%29%2Cg%28x%29%2Cx%E2%88%88R%E6%BB%A1%E8%B6%B3%E6%9D%A1%E4%BB%B6%3Ab1%3Db%2Can%3Df%28bn%29%3Dg%28b%28n%2B1%29%29%28n%E2%88%88N%2A%29%E8%8B%A5f%28x%29%3Dtx%2B1%28t%E2%89%A00%2Ct%E2%89%A02%29%2Cg%28x%29%3D2x%2Cf%28b%29%E2%89%A0g%28b%29%2C%E4%B8%94lim%28an%29%28n%E2%86%92%E2%88%9E%29%E5%AD%98%E5%9C%A8%2C%E6%B1%82t%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%2C%E5%B9%B6%E6%B1%82lim%28an%29%28n%E2%86%92%E2%88%9E%29%28%E7%94%A8t%E8%A1%A8%E7%A4%BA%29.)
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