document.write( "Question 1184007: prove by mathematical induction:
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Algebra.Com's Answer #814546 by math_helper(2461) $\"\"$ $\"About$

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prove by mathematical induction:
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document.write( "Base case:   = 1
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document.write( "             =  = 1\r
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document.write( "Base case holds.\r
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document.write( "Hypothesis:  
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document.write( "Assume  + ... +  =  for n=k.  (*)\r
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document.write( "Step case:  Let n=k+1
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document.write( " [  + ... +  ] +  \r
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document.write( "... use hypothesis on terms within [  ] ...\r
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document.write( "=  + \r
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document.write( "... this reduces to (you can factor  then use a factoring website for the rest) ...  (see NOTE)\r
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document.write( "= \r
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document.write( "The proof is complete here, but it is not obvious, so
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document.write( "let u=k+1 --> k=u-1\r
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document.write( "= 
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document.write( "= \r
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document.write( "Proof complete\r
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document.write( "NOTE:  I admit, there may be an easier path here.  If other tutors (or the student) wish to find it, more power to them.  I gave the general idea...\r
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document.write( "If this helps the student, thanks are appreciated.  
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