Could anyone suggest a neat way to proving that the Harmonic Series, Hn=1+1/2+1/3+1/4+...+1/n is bounded by ln(n){lower bound} and ln(n)+1{upper bound} ? ln is the natural logarithm.
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Originally Posted by p vs np Could anyone suggest a neat way to proving that the Harmonic Series, Hn=1+1/2+1/3+1/4+...+1/n is bounded by ln(n){lower bound} and ln(n)+1{upper bound} ? ln is the natural logarithm. Read this: http://faculty.prairiestate.edu/skifowit/htdocs/sd1.pdf
Originally Posted by p vs np Could anyone suggest a neat way to proving that the Harmonic Series, Hn=1+1/2+1/3+1/4+...+1/n is bounded by ln(n){lower bound} and ln(n)+1{upper bound} ? ln is the natural logarithm. it's clear for n = 1. for n > 1 write mean value theorem for on the interval to get: for some therefore: hence: which gives us: thus: which is a better result than what you asked!
Compact and elegant. Thanks
here's another way of proving those bounds: for each is now it's on the other hand is finally it's
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