wu :: forums « wu :: forums - Summation » Welcome, Guest. Please Login or Register. Nov 28th, 2024, 10:10am

RIDDLES SITE WRITE MATH! Home Help Search Members Login Register

wu :: forums    riddles    medium (Moderators: william wu, towr, Icarus, Grimbal, SMQ, Eigenray, ThudnBlunder)    Summation « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Summation  (Read 821 times) ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Summation   « on: Apr 23rd, 2010, 2:52pm » Quote Modify Find (without programming) the greatest integer less than 1 + 1/2 + 1/3 + ....... + 1/1000000 IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Obob Senior Riddler     Gender: Posts: 489 Re: Summation   « Reply #1 on: Apr 23rd, 2010, 3:12pm » Quote Modify Given some calculus, it's not so hard to guess the right answer.  Proving it is correct (without actually finding the sum) could be much more difficult, though... IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Summation   « Reply #2 on: Apr 23rd, 2010, 3:14pm » Quote Modify Through integration you can find an upper limit of 1999, and a lower limit slightly over 1998, so 1998 must be the greatest integer that's less IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Obob Senior Riddler     Gender: Posts: 489 Re: Summation   « Reply #3 on: Apr 23rd, 2010, 3:18pm » Quote Modify Ah, good call on the upper bound. IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Summation   « Reply #4 on: Apr 23rd, 2010, 3:40pm » Quote Modify Actually, without calculus the sum telescopes nicely if successive terms are 'inverted' somehow.     IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Aryabhatta Uberpuzzler     Gender: Posts: 1321 Re: Summation   « Reply #5 on: Apr 23rd, 2010, 7:45pm » Quote Modify For a without calculus solution, use the following:   1/sqrt(n) >= 2(sqrt(n+1) - sqrt(n)) >= 1/sqrt(n+1) IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board