数列1/n怎么求和数列为｛1/n｝，求此数列前n 数列1/n怎么求和
\u6570\u52171/n\u600e\u4e48\u6c42\u548c\u6570\u5217\u4e3a\uff5b1/n\uff5d\uff0c\u6c42\u6b64\u6570\u5217\u4f60\u597d\uff0c\u8fd9\u662f\u6570\u5b66\u7ade\u8d5b\u7684\u516c\u5f0f\uff0c\u5475\u5475\uff0c\u80fd\u67e5\u5230 \u8c03\u548c\u7ea7\u6570\uff0c\u7f51\u4e0a\u7684\u8fc7\u7a0b\u5f88\u8be6\u7ec6\uff0c\u5e0c\u671b\u5bf9\u4f60\u6709\u5e2e\u52a9\u3002
\u5f53n\u5f88\u5927\u65f6\uff0c\u6709\uff1a1+1/2+1/3+1/4+1/5+1/6+...1/n = 0.57721566490153286060651209 + ln(n)//C++\u91cc\u9762\u7528log(n)\uff0cpascal\u91cc\u9762\u7528ln(n)
0.57721566490153286060651209\u53eb\u505a\u6b27\u62c9\u5e38\u6570
to GXQ:
\u5047\u8bbe;s(n)=1+1/2+1/3+1/4+..1/n
\u5f53 n\u5f88\u5927\u65f6 sqrt(n+1)
= sqrt(n*(1+1/n))
= sqrt(n)*sqrt(1+1/2n)
\u2248 sqrt(n)*(1+ 1/(2n))
= sqrt(n)+ 1/(2*sqrt(n))
\u8bbe s(n)=sqrt(n),
\u56e0\u4e3a\uff1a1/(n+1)<1/(2*sqrt(n))
\u6240\u4ee5\uff1a
s(n+1)=s(n)+1/(n+1)< s(n)+1/(2*sqrt(n))
\u5373\u6c42\u5f97s(n)\u7684\u4e0a\u9650
1+1/2+1/3+\u2026+1/n\u662f\u6ca1\u6709\u597d\u7684\u8ba1\u7b97\u516c\u5f0f\u7684\uff0c\u6240\u6709\u8ba1\u7b97\u516c\u5f0f\u90fd\u662f\u8ba1\u7b97\u8fd1\u4f3c\u503c\u7684\uff0c\u4e14\u7cbe\u786e\u5ea6\u4e0d\u9ad8\u3002
\u81ea\u7136\u6570\u7684\u5012\u6570\u7ec4\u6210\u7684\u6570\u5217,\u79f0\u4e3a\u8c03\u548c\u6570\u5217.\u4eba\u4eec\u5df2\u7ecf\u7814\u7a76\u5b83\u51e0\u767e\u5e74\u4e86.\u4f46\u662f\u8fc4\u4eca\u4e3a\u6b62\u6ca1\u6709\u80fd\u5f97\u5230\u5b83\u7684\u6c42\u548c\u516c\u5f0f\u53ea\u662f\u5f97\u5230\u5b83\u7684\u8fd1\u4f3c\u516c\u5f0f(\u5f53n\u5f88\u5927\u65f6):
1+1/2+1/3+......+1/n\u2248lnn+C(C=0.57722......\u4e00\u4e2a\u65e0\u7406\u6570,\u79f0\u4f5c\u6b27\u62c9\u521d\u59cb,\u4e13\u4e3a\u8c03\u548c\u7ea7\u6570\u6240\u7528)
\u4eba\u4eec\u503e\u5411\u4e8e\u8ba4\u4e3a\u5b83\u6ca1\u6709\u4e00\u4e2a\u7b80\u6d01\u7684\u6c42\u548c\u516c\u5f0f.
\u4f46\u662f,\u4e0d\u662f\u56e0\u4e3a\u5b83\u662f\u53d1\u6563\u7684,\u624d\u6ca1\u6709\u6c42\u548c\u516c\u5f0f.\u76f8\u53cd\u7684,\u4f8b\u5982\u7b49\u5dee\u6570\u5217\u662f\u53d1\u6563\u7684,\u516c\u6bd4\u7684\u7edd\u5bf9\u503c\u5927\u4e8e1\u7684\u7b49\u6bd4\u6570\u5217\u4e5f\u662f\u53d1\u6563\u7684,\u5b83\u4eec\u90fd\u6709\u6c42\u548c\u516c\u5f0f.
1+1/2+1/3+1/4+...1/n = ln(n+1) + r
r：欧拉常数，约为0.577218
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