证明数列1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)有极限

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证明数列1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)有极限
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证明数列1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)有极限
证明数列1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)有极限

证明数列1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)有极限
设f(n)=1+1/3+1/5+…+1/(2n+1)-0.5*ln(n+1)
f(n+1)-f(n)=1/(2n+3)-0.5*ln(n+2)+0.5*ln(n+1)
=1/(2n+3)-0.5*ln(1+1/(n+1))
下面证明ln(1+x)>x/(x+1) (0