Unformatted text preview: ¹ ( n âˆ’ 1) + 3 È¹ n ( n + 1)( n + 2)
( n âˆ’ 1) n ( n + 1)
+ n ( n + 1) = n ( n + 1)È¹ È¹ =
â‚¬
È¹ Èº
3
3
3
and this equals the right hand side of the equation to be proved. QED Question 2: Prove by induction: â‚¬
For all integers n â‰¥1, the integer 5n â€“ 1 is divisible by 4. PROOF: Proof by induction. The statement above is true when n= 1: For 51 â€“ 1 = 4, which is divisible by 4. Assume True: 5n â€“ 1 is divisible by 4. This means that 5n â€“ 1 = 4a for an integer a. Then Prove: 5n...
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This note was uploaded on 01/29/2014 for the course MATH 300A taught by Professor Jamesking during the Winter '11 term at University of Washington.
 Winter '11
 JamesKing
 Math, Integers

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