Clear["`*"]RSolve[{a[n] == 1/2 (a[n - 1] + 3/a[n - 1]), a[0] == 1}, a[n], n] (*求出数列的通项公式*)a[n_] := Sqrt[3] Coth[2^n ArcCoth[1/Sqrt[3]]] (*定义数列的通项公式为新的函数*)Limit[a[n], n -> Infinity ] (*求数列的极限*)N[Sum[a[n], {n, 1, 30}]] (*前30项的和*)ListPlot[Table[a[n], {n, 30}]] (*散点图*)
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