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[50] Homework 4.
Proof Techniques
Each problem is worth 10 points
[10] Show that
3
√
3 is irrational.
[10] Prove that for positive integer
n
,
n
3
+ 2
n
is divisible by 3.
[10] Using mathematical induction prove that
n
s
i
=1
i
2
i
= 2
n
+1
(
n

1) + 2
.
[10] DeFne the
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Unformatted text preview: n th Harmonic number as H n = n s i =1 1 i . Prove by induction on n ≥ 0 that H 2 n ≥ 1 + n 2 . [10] Derive an explicit formula for the following recurrence for n ≥ 1 a n = n 2 a n1 with a = 1. 1...
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This note was uploaded on 03/26/2012 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue University.
 Spring '08
 Staff
 Statistics

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