| [ QuizWit ] in KIDS 글 쓴 이(By): iLUSiON (띠띠빤쮸) 날 짜 (Date): 2005년 12월 15일 목요일 오후 07시 21분 01초 제 목(Title): Re: [Q] 1에서 n까지 자연수의 역수의합... haha.... it's 4:30 in the morning and i haven't slept all night. just solved a complicated problem that bugged me a couple of months.... so happy.... anywayy let's see killer's problem... why don't we multiply n! and see what happens ^^ then we have 1+1/2 +... 1/n = (bla bla)/n! now this bla bla is smaller than n*n!. Hence the whole thing is smaller than n. Now if the number is an integer between 2 and n, it must be divided by one of numbers between 2 and n. damn i don't think this works.. haha.... let me try one morer time. ^^ this is related to an integral of 1/x. Do Riemann sum thingy.... then 1/2 + 1/3 + ...1/n < ln n < 1 + 1/2 + .... + 1/(n-1) so 1+ 1/2 + ...1/n is between ln n + 1/n and ln n + 1. for large n, i am sure this nummber can't be integer. now send me ppe-ppe-ro ^^ nice problem thou... iLUSiON - le plus grand de tous http://cyworld.nate.com/ilusion |