ln 2/2^2+ln 3/3^2+ln 4/4^2+.+ln n/n^2=ln(1/2*1/3*1/4*...1/(n-1)*1/n)=ln(1/n!)2(√n - 1)/√n=2√n-2/√n=2-2/√n∵n!趋于无穷大,而ln底数>2,∴ln(1/n!)0∴ln 2/2^2+ln 3/3^2+ln 4/4^2+.+ln n/n^2...