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Last edited by tomatoe; March 15th 2007 at 08:55 PM.
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Originally Posted by tomatoe 1) Prove that if lim n approaches infinity absolute value of "a sub n + 1" over "a sub n" = L < 1, then the lim n approach infinity of "a sub n" = 0. Choose L<a<1. Now (L-a)/2 > 0 Thus, ||a_{n+1}/a_n| - L|<(L-a)/2 (L-a)/2-L<|a_{n+1}/a_n|<(L-a)/2+L |a_{n+1}/a_n|<(L+a)/2<(a+a)/2=a. Thus, |a_{n+1}|<a*|a_n| for n>N Use that to construct a geometric sequence.
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