求证:2(1/3+1/5+1/7+……+1/(2n-1))
问题描述:
求证:2(1/3+1/5+1/7+……+1/(2n-1))
答
2/(2k+1)=∫((2k-1),(2k+1))1/(2k+1)dx≤∫((2k-1),(2k+1))1/xdx
2(1/3+1/5+1/7+……+1/(2n+1))≤∫(1,(2k+1))1/xdx=lnx︱(1,(2k+1))=ln(2k+1)