在数列{an},{bn}中,a1=2,b1=4,且an,bn,a(n+1)成等差数列,bn,a(n+1),b(n+1)成等比数列(n€n*)1)求a2,a3,a4及b1,b2,b3,由此猜测{an},{bn}的通项公式;2)证明:1/(a1+b1)+1/(a2+b2)+1/(a3+b3)+~+1/(an+bn)
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![在数列{an},{bn}中,a1=2,b1=4,且an,bn,a(n+1)成等差数列,bn,a(n+1),b(n+1)成等比数列(n€n*)1)求a2,a3,a4及b1,b2,b3,由此猜测{an},{bn}的通项公式;2)证明:1/(a1+b1)+1/(a2+b2)+1/(a3+b3)+~+1/(an+bn)](/uploads/image/z/1549918-46-8.jpg?t=%E5%9C%A8%E6%95%B0%E5%88%97%7Ban%7D%2C%7Bbn%7D%E4%B8%AD%2Ca1%3D2%2Cb1%3D4%2C%E4%B8%94an%2Cbn%2Ca%28n%2B1%29%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2Cbn%2Ca%28n%2B1%29%2Cb%28n%2B1%29%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%EF%BC%88n%26%238364%3Bn%2A%291%EF%BC%89%E6%B1%82a2%2Ca3%2Ca4%E5%8F%8Ab1%2Cb2%2Cb3%2C%E7%94%B1%E6%AD%A4%E7%8C%9C%E6%B5%8B%7Ban%7D%2C%7Bbn%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%9B2%EF%BC%89%E8%AF%81%E6%98%8E%EF%BC%9A1%2F%28a1%2Bb1%29%2B1%2F%28a2%2Bb2%29%2B1%2F%28a3%2Bb3%29%2B%7E%2B1%2F%28an%2Bbn%29)
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