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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 (
n
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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 ( n1) + F ( n2) ,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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This note was uploaded on 03/07/2010 for the course MA 2312 taught by Professor Johniacono during the Spring '10 term at NYU Poly.
 Spring '10
 JohnIacono
 Math

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