1.已知函数g(x)=(根号x+2)²,(x≥0),数列{an}满足a1=1,an+1=g(an)(n∈N+) (1)求数列{an}的通项公式(2)记Tn=1/a1+1/a2+…+1/an(n≥2),求证:Tn+1/2(2n+1)>7/62.已知数列{an}中,a1=1,且点P(an,an+1)(n∈N+)在一次函数y=x+1
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![1.已知函数g(x)=(根号x+2)²,(x≥0),数列{an}满足a1=1,an+1=g(an)(n∈N+) (1)求数列{an}的通项公式(2)记Tn=1/a1+1/a2+…+1/an(n≥2),求证:Tn+1/2(2n+1)>7/62.已知数列{an}中,a1=1,且点P(an,an+1)(n∈N+)在一次函数y=x+1](/uploads/image/z/4021327-55-7.jpg?t=1.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0g%28x%29%3D%28%E6%A0%B9%E5%8F%B7x%2B2%29%26%23178%3B%2C%28x%E2%89%A50%29%2C%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2Can%2B1%3Dg%28an%29%28n%E2%88%88N%2B%29+%281%29%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%282%29%E8%AE%B0Tn%3D1%2Fa1%2B1%2Fa2%2B%E2%80%A6%2B1%2Fan%28n%E2%89%A52%29%2C%E6%B1%82%E8%AF%81%EF%BC%9ATn%2B1%2F2%282n%2B1%29%3E7%2F62.%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Ca1%3D1%2C%E4%B8%94%E7%82%B9P%EF%BC%88an%2Can%2B1%29%28n%E2%88%88N%2B%29%E5%9C%A8%E4%B8%80%E6%AC%A1%E5%87%BD%E6%95%B0y%3Dx%2B1)
1.已知函数g(x)=(根号x+2)²,(x≥0),数列{an}满足a1=1,an+1=g(an)(n∈N+) (1)求数列{an}的通项公式(2)记Tn=1/a1+1/a2+…+1/an(n≥2),求证:Tn+1/2(2n+1)>7/62.已知数列{an}中,a1=1,且点P(an,an+1)(n∈N+)在一次函数y=x+1
1.已知函数g(x)=(根号x+2)²,(x≥0),数列{an}满足a1=1,an+1=g(an)(n∈N+) (1)求数列{an}的通项公式
(2)记Tn=1/a1+1/a2+…+1/an(n≥2),求证:Tn+1/2(2n+1)>7/6
2.已知数列{an}中,a1=1,且点P(an,an+1)(n∈N+)在一次函数y=x+1的图像上.
(1)求数列{an}的通项公式
(2)若函数f(n)=1/(n+a1)+1/(n+a2)+…+1/(n+an)(n∈N+,n≥2),求函数f(n)的最小值;
(3)设bn=1/an,Sn表示数列{bn}的前n项和.试问:是否存在关于n的整式g(n),使得S1+S2+S3+…+Sn-1=(Sn-1)g(n)对一切不小于2的自然数n均成立?若存在,写出g(n)的解析式,并加以证明;若不存在,请说明理由.
第二题我会了,只求第一题第二问
1.已知函数g(x)=(根号x+2)²,(x≥0),数列{an}满足a1=1,an+1=g(an)(n∈N+) (1)求数列{an}的通项公式(2)记Tn=1/a1+1/a2+…+1/an(n≥2),求证:Tn+1/2(2n+1)>7/62.已知数列{an}中,a1=1,且点P(an,an+1)(n∈N+)在一次函数y=x+1
直接用数学归纳法证明.