You can put this solution on YOUR website! : Show by the Principle of Mathematical Induction:
5n – 1 is divisible by 2 for all n>=1
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Show it is true for n = 1
5*1-1 = 4 = 2*2
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Assume it is true for n = k
5^k-1 is divisible by 2
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Show it must be true for n = k+1
5^(k+1)-1 = 5^k *5 -1 = 4*5^k * 5^k -1 = 2(2*5^k) + 5^k-1
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Conclusion:: Since 5^k-1 is divisible by 2 and 2(2*5^k) is divisble
by 2, 5^(k+1)-1 is divisible by 2.
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Cheers,
Stan H.
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