P(n)推导已知p(1)=1;p(n)=(1-1/(n^2))p(n-1)+2/n-1/(n^2);请由递推公式推导出p(n)的表达式提示:p(n)=2*(n+1)/n*(1/2+1/3+.+1/(n+1))-1;p(n)递推公式p(n)=(1-1/(n^2))p(n-1)+(2/n)-1/(n^2);
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![P(n)推导已知p(1)=1;p(n)=(1-1/(n^2))p(n-1)+2/n-1/(n^2);请由递推公式推导出p(n)的表达式提示:p(n)=2*(n+1)/n*(1/2+1/3+.+1/(n+1))-1;p(n)递推公式p(n)=(1-1/(n^2))p(n-1)+(2/n)-1/(n^2);](/uploads/image/z/11663492-68-2.jpg?t=P%28n%29%E6%8E%A8%E5%AF%BC%E5%B7%B2%E7%9F%A5p%281%29%3D1%3Bp%28n%29%3D%281-1%2F%28n%5E2%29%29p%28n-1%29%2B2%2Fn-1%2F%28n%5E2%29%3B%E8%AF%B7%E7%94%B1%E9%80%92%E6%8E%A8%E5%85%AC%E5%BC%8F%E6%8E%A8%E5%AF%BC%E5%87%BAp%28n%29%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F%E6%8F%90%E7%A4%BA%EF%BC%9Ap%28n%29%3D2%2A%28n%2B1%29%2Fn%2A%281%2F2%2B1%2F3%2B.%2B1%2F%28n%2B1%29%29-1%3Bp%28n%29%E9%80%92%E6%8E%A8%E5%85%AC%E5%BC%8Fp%28n%29%3D%281-1%2F%28n%5E2%29%29p%28n-1%29%2B%282%2Fn%29-1%2F%28n%5E2%29%3B)
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