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Assignment - Homework 5

Assignment - Homework 5 - 2 n 2 2 regions if no two lines...

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MA2312 Homework 5 John Iacono February 24, 2010 1. Prove by induction, that for all integer n where n > 1 n X i =1 1 i 2 < 2 - 1 n 2. Prove by induction, that for all integer n where n 1 n X i =1 i ( i + 1)( i + 2) = n ( n + 1)( n + 2)( n + 3) 4 3. Prove by induction, that for all integer n where n 1 n X i =1 i i Y j =1 j = n +1 Y i =1 i - 1 4. Prove by induction, that n lines separate the plane into (
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Unformatted text preview: 2 + n + 2) / 2 regions if no two lines are parallel and no three lines intersect in a common point. 5. Let F (0) = 0 ,F (1) = 1 and F ( n ) = F ( n-1) + F ( n-2) ,n ≥ 2. Prove there is some c that by induction for all integer n > c , 1 . 5 n < F ( n ) < 2 n < n ! < n n 1...
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