高中有点难度的数列设数列{an}的各项都是正数,且对任意n∈N*都有a1^3+a2^3+a3^3=(Sn)^2,记Sn为数列{an}的前n项和(1)求证:an^2=2Sn-an(2){an}的通项公式(3)若bn=3^n+(-1)^(n-1)*k*2^an(k为非零常数,n∈N*)问
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![高中有点难度的数列设数列{an}的各项都是正数,且对任意n∈N*都有a1^3+a2^3+a3^3=(Sn)^2,记Sn为数列{an}的前n项和(1)求证:an^2=2Sn-an(2){an}的通项公式(3)若bn=3^n+(-1)^(n-1)*k*2^an(k为非零常数,n∈N*)问](/uploads/image/z/1159635-3-5.jpg?t=%E9%AB%98%E4%B8%AD%E6%9C%89%E7%82%B9%E9%9A%BE%E5%BA%A6%E7%9A%84%E6%95%B0%E5%88%97%E8%AE%BE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%90%84%E9%A1%B9%E9%83%BD%E6%98%AF%E6%AD%A3%E6%95%B0%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8Fn%E2%88%88N%2A%E9%83%BD%E6%9C%89a1%5E3%2Ba2%5E3%2Ba3%5E3%3D%28Sn%29%5E2%2C%E8%AE%B0Sn%E4%B8%BA%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%281%29%E6%B1%82%E8%AF%81%EF%BC%9Aan%5E2%3D2Sn-an%282%29%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%883%EF%BC%89%E8%8B%A5bn%3D3%5En%2B%28-1%29%5E%EF%BC%88n-1%EF%BC%89%2Ak%2A2%5Ean%28k%E4%B8%BA%E9%9D%9E%E9%9B%B6%E5%B8%B8%E6%95%B0%2Cn%E2%88%88N%2A%29%E9%97%AE)
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