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ma6021HandOut3
Course: MATH 6021, Summer 2009School: Georgia Tech
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6021 Math Let a and b be two strictly positive real numbers. 2ab a+b ab . 1) Show that a+b 2 2) Define a0 = a and b0 = b and put an+1 = 2an bn an + b n and bn+1 = Summer 2007 - Handout #3 an + b n , 2 n 0. Show that for n 1 we have a1 a 2 a n n b b 2 b 1 and that an bn = a0 b0 = ab ab. Show 3) Show that the sequences {an } and {bn } converge to the same limit, namely moreover that for...
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6021 Math Let a and b be two strictly positive real numbers. 2ab a+b ab . 1) Show that a+b 2 2) Define a0 = a and b0 = b and put an+1 = 2an bn an + b n and bn+1 =
Summer 2007 - Handout #3
an + b n , 2
n 0.
Show that for n 1 we have a1 a 2 a n n b b 2 b 1 and that an bn = a0 b0 = ab ab. Show
3) Show that the sequences {an } and {bn } converge to the same limit, namely moreover that ...
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