document.write( "Question 1149333: 1^2+3^2+...+(2n-1)^2=1/3n(4n^2-1) \n" ); document.write( "

Algebra.Com's Answer #770678 by math_helper(2461) $\"\"$ $\"About$

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document.write( "n=1:     &   \r
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document.write( "Assume  + ... +  =  for n=k\r
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document.write( "Let n=k+1:\r
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document.write( "  + ... +   +  \r
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document.write( "// Apply hypothesis to all but the last term 
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document.write( "=  + \r
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document.write( "// combine
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document.write( "= \r
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document.write( "// Here you can attempt to factor, or, you can see if (1/3)(k+1)(4(k+1)^2-1)
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document.write( "// expands to the same expression...  I will do the latter approach...\r
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document.write( "= 
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document.write( "= 
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document.write( "= \r
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document.write( "They match, the hypothesis is also true for n=k+1, DONE.
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