求数列的极限怎么求，过程详细点，谢谢 求数列极限？化简步骤请详细一点，谢谢各位老师指导！
\u6c42\u8fd9\u4e2a\u6570\u5217\u7684\u6781\u9650(\u8fc7\u7a0b\u5c3d\u91cf\u8be6\u7ec6\u70b9)\u8fd9\u4e2a\u6570\u5217\u7684\u9012\u63a8\u516c\u5f0f\u662fx[n]=2+1/x[n-1]
\u82e5n\u2192\u221e\u6781\u9650\u5b58\u5728\uff0c\u5219\u6b64\u65f6x[n]=x[n-1]\uff0c\u4e8e\u662f\u9012\u63a8\u5f0f\u53d8\u6210\u4e86\u65b9\u7a0bx=2+1/x\uff0c\u89e3\u51fa\u6765\u5f97x=1+\u221a2
\u5c31\u662f\u6570\u5217\u7684\u6781\u9650
1\u3001\u62ec\u53f7\u91cc=[(1+n)n/2]\u00f7n²=(1+n)/(2n)=1/(2n)\uff0b1/2 \u6240\u4ee5\u6781\u9650\u4e3a1/2
2\u3001Xn+1\u5bf9Xn\u6c42\u5bfc\uff0c\u5927\u4e8e0\uff0c\u8bf4\u660eXn+1\u4e0eXn\u540c\u589e\u540c\u51cf\uff0cX2=4\uff0c\u6240\u4ee5\u6570\u5217\u5355\u8c03\u9012\u51cf\u3002\u800c\u4e14\u5404\u9879\u5927\u4e8e0\u3002\u7531\u5355\u8c03\u6709\u754c\u5b9a\u7406\uff0c\u6570\u5217\u6709\u6781\u9650
3\u3001\u221a(n²+3)\uff0fn\uff1d\u221a(1+3/n²)\uff1c\u221a1\uff0b\u221a\uff083/n²\uff09
\u5bf9E\u03b5\ufe650\uff0c\u5b58\u5728N=\u221a3/\u03b5,\u5f53n\uff1eN\u65f6\uff0c|\u221a(n²+3)\uff0fn\uff0d1|\uff1c\u221a1\uff0b\u221a\uff083/n²\uff09-1=\u03b5
\u6240\u4ee5\u6781\u9650\u4e3a1
第五题：同第一题，分开两项求解，第一项的极限为1本身，第二项极限为0。结果为1
1.
lim (1+n)/n^2
=lim (1+n)/n / n^2/n
=lim (1+1/n) * lim 1/n
=1*0
=0
5.
lim 1+1/2^n
=1+lim 1/2^n
=1+0
1
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