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Mathematics Forum
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| Author | Message / Information |
| jamesdoinghwk Quote | Reply | | weird sequence quesiton posted on: 4/6/2007 3:42:38 PM Denoting the nth term in the sequence 1, 3, 4, 7, 11, 29, 47, 76 by a to the subscript n, prove that a to the subscript n is less than (7/4)^n for every positive integer n. THen derive an explicit formula for a to the subscript n and determine its limit as n approaches infinity. So this question involves a proof which isn't too hard, say n = k, prove it is true for k = 1 lowest value of k, then prove it is true for k + 1 and thus by induction it is true for all values of n. The explict formula the closest I've gotten to is (7/4)^n-1 true for 1 and 3 but not 4... but once i get the formula i can find the limit. Can anyone help? |
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