document.write( "Question 1057029: Proof that the sums of the first N Square Numbers is given by
\n" ); document.write( " =[n(n+1)(2n+1)]/6 \n" ); document.write( "
Algebra.Com's Answer #672113 by stanbon(75887)\"\" \"About 
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Proof that the sums of the first N Square Numbers is given by
\n" ); document.write( "=[n(n+1)(2n+1)]/6
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\n" ); document.write( "Show it's true for n = 1::
\n" ); document.write( "1 = [1(2)(3)]/6
\n" ); document.write( "1 = 1
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\n" ); document.write( "Assume it's true for n = k::
\n" ); document.write( "1 + 4 + 9 +...k^2 = [k(k+1)(2k+1)]/6
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\n" ); document.write( "Show it is true for n = k+1
\n" ); document.write( "---
\n" ); document.write( "1 + 4 + 9 + .. k^2 + (k+1)^2
\n" ); document.write( "----
\n" ); document.write( "= [k(k+1)(2k+1)]/6 + (k+1)^2
\n" ); document.write( "-----
\n" ); document.write( "= [(k+1)[k(2k+1)]/6+(k+1)]
\n" ); document.write( "-------
\n" ); document.write( "= [(k+1)[2k^2 + k + 6k + 6]/6
\n" ); document.write( "= [(k+1)(2k^2 + 7k + 6]/6
\n" ); document.write( "= [(k+1)[(2k^2+ 4k + 3k + 6]/6
\n" ); document.write( "-----
\n" ); document.write( "= [(k+1)[2k(k+2)+3(k+2)]/6
\n" ); document.write( "= [(k+1)[(2k+3)(k+2)]/6
\n" ); document.write( "= [(k+1)(2(k+1)+1)((k+1)+1]/6
\n" ); document.write( "----
\n" ); document.write( "= [(k+1)((k+1)+1)(2(k+1)+1]/6
\n" ); document.write( "------------------
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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