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CTK Exchange
Becca
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Feb-23-06, 07:01 AM (EST) |
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"URGENT HELP NEEDED for Induction and Divisibility"
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Use mathematical induction to prove that 5^n + 9^n +2 is divisible by 4 (n belongs to all positive integers). ok this is what i've got so far: assume that the statement is true for n=k let n=k+1 5^(k+1) + 9^(k+1) + 2
(5^k)*5 + (9^k)*9 + 2 and where do i go from here? anyone? |
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herman hofstede
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Feb-24-06, 09:02 AM (EST) |
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2. "RE: URGENT HELP NEEDED for Induction and Divisibility"
In response to message #0
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5*5^n+9*9^n+2
= 4*5^n+5^n + 8*9^n+9^n+2
= 4*5^n + 8*9^n + (5^n + 9^n + 2)
= 4*5^n + 4*2*8^n + (5^n + 9^n + 2)
= 4*(5^n + 2*9^n) + (5^n + 9^n +2)
the first term is divisible by 4
the second term is divisible by 4 (induction-step)
so the sum is divisible by 4.
q.e.d. |
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