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h4 - n th Harmonic number as H n = n s i =1 1 i Prove by...

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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 summationdisplay i =1 i 2 i = 2 n +1 ( n - 1) + 2 . [10] Define 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 n-1 with a = 1. 1...
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