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Do you have to use the induction hypothesis when proving by induction? (1 Viewer)

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calamebe

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Title, I was just doing an induction proof (which could easily be done algebraically anyway) and while proving for n=k+1, I could prove it either by using the induction hypothesis or just algebra. I didn't know whether I had to use the induction hypothesis or not, so just asking here. Thanks in advance!
 
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InteGrand

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calamebe said:
Title, I was just doing an induction proof (which could easily be done algebraically anyway) and while proving for n=k+1, I could prove it either by using the induction hypothesis or just algebra. I didn't know whether I had to use the induction hypothesis or not, so just asking here. Thanks in advance!
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Yes, you need to use the inductive hypothesis to make it a proof by induction. If you didn't make use of it, then you have essentially proved the statement without induction.
 
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