EventHorizon Posted March 26, 2008 Report Share Posted March 26, 2008 What is the sum of this series equal to in the limit? 2/100, 4/10000, 8/10^6, 16/10^8, 32/10^10, ... Yeah....its a simple geometric series....but it is kinda interesting when you multiply each term by 7 and see what the sum is equal to. Quote Link to comment Share on other sites More sharing options...
0 unreality Posted March 26, 2008 Report Share Posted March 26, 2008 from what I can tell the nth term is 2n/102n Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 26, 2008 Report Share Posted March 26, 2008 I forgot the formulae of geometric series..and i am too lazy to get help from the net Quote Link to comment Share on other sites More sharing options...
0 EventHorizon Posted March 26, 2008 Author Report Share Posted March 26, 2008 from what I can tell the nth term is 2n/102n That's right, though it can be simplified to a simple power of a fraction. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 26, 2008 Report Share Posted March 26, 2008 What is the sum of this series equal to in the limit? 2/100, 4/10000, 8/10^6, 16/10^8, 32/10^10, ... Yeah....its a simple geometric series....but it is kinda interesting when you multiply each term by 7 and see what the sum is equal to.The sum is 1/49. Multiplying by 7 gives 1/7. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 26, 2008 Report Share Posted March 26, 2008 the sum is 1/49...if you multiply it with 7, it will be 1/7...if you multiply with 72 it will be 1 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 26, 2008 Report Share Posted March 26, 2008 the sum is 1/49...if you multiply it with 7, it will be 1/7...if you multiply with 72 it will be 1 So, echo ... guess you looked the formula up after all. Quote Link to comment Share on other sites More sharing options...
0 EventHorizon Posted March 26, 2008 Author Report Share Posted March 26, 2008 the decimal expansion of 1/7 = .142857142857142857... 14 = (7*2) 28 = (7*4) 56 = (7*8) 112 = (7*16) etc. At least it is an easy way to remember what 1/7th is equal to. Quote Link to comment Share on other sites More sharing options...
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EventHorizon
What is the sum of this series equal to in the limit?
2/100, 4/10000, 8/10^6, 16/10^8, 32/10^10, ...
Yeah....its a simple geometric series....but it is kinda interesting when you multiply each term by 7 and see what the sum is equal to.
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