Show 1 more comment. Active Oldest Votes. This proof is often attributed to Nicole Oresme. Tunk-Fey AgCl AgCl 5, 7 7 gold badges 37 37 silver badges 37 37 bronze badges.
Wikipedia has a nice display of this proof [ en. Show 4 more comments. EDIT It seems the original link is broken, due to the author moving to his own site. Kifowit and Terra A. Add a comment.
Ian Mateus Ian Mateus 6, 3 3 gold badges 29 29 silver badges 54 54 bronze badges. And possibly pedagogically best; I don't know. Dominic Michaelis Khosrotash Khosrotash What's the reasoning their Noah Snyder Noah Snyder 9, 3 3 gold badges 36 36 silver badges 58 58 bronze badges.
I was hoping to avoid an answer that involved integration, so I also prefer AgCl's answer. The proof is complete. Teoc 8, 3 3 gold badges 22 22 silver badges 55 55 bronze badges. Ahaan S. Rungta Ahaan S. Rungta 7, 5 5 gold badges 25 25 silver badges 63 63 bronze badges. Rasmus Erlemann Rasmus Erlemann 2, 2 2 gold badges 16 16 silver badges 30 30 bronze badges. Then this contradiction shows that the series diverges. Jose Antonio Jose Antonio 6, 2 2 gold badges 23 23 silver badges 37 37 bronze badges.
Squirtle Squirtle 6, 27 27 silver badges 55 55 bronze badges. Ryan Reich Ryan Reich 6, 19 19 silver badges 30 30 bronze badges. The reason that it does not work is because the number of terms is infinite. All you've proven is that the second series approaches the final value faster than the first one. But whether this value is ultimately finite or not, you have not shown. The student's question was Community Bot 1. Matt Rigby Matt Rigby 2, 10 10 silver badges 13 13 bronze badges.
User User Come on! The last inequality itself is proof enough!! Alex Peter Alex Peter 5 5 silver badges 7 7 bronze badges. Ali Shadhar Ali Shadhar Micah Micah Barry Cipra Barry Cipra 77k 7 7 gold badges 71 71 silver badges bronze badges.
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The unofficial elections nomination post. Active 18 days ago. Viewed k times. Hossien Sahebjame 5 5 silver badges 15 15 bronze badges. You should probably revise the topic. The OP probably won't see this comment anyway, as they have not logged in recently.
Add a comment. Active Oldest Votes. Community Bot 1. Charles Charles A recent related idea for a first year calculus exercise: An intelligent robot named Marvin travelled back in time to the moment of the Big Bang Jyrki Lahtonen.
I believe the OP meant decreasing to 0. The rate of growth is the derivative. Qiaochu Yuan Qiaochu Yuan k 41 41 gold badges silver badges bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Linked 5. Related 9. Hot Network Questions.
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