document.write( "Question 1104788: use the principals of mathematical induction to prove the following statement 1+5+5^2+...+5^n-1 = 1/4(5n-1) \r
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Algebra.Com's Answer #719481 by math_helper(2461)\"\" \"About 
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use the principals of mathematical induction to prove the following statement 1+5+5^2+...+5^n-1 = 1/4(5n-1) \r
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\n" ); document.write( "The right hand side is not correct. It should be \"+%281%2F4%29%285%5En+-+1%29+\"
\n" ); document.write( "Let \"+S%5Bn%5D+\" = partial sum n (where \"5%5E%28n-1%29+\" is the highest power in the sum)\r
\n" ); document.write( "\n" ); document.write( "Proof by induction:
\n" ); document.write( "\"+S%5B1%5D+=+1+=+%281%2F4%29%285%5E1+-+1%29+\"
\n" ); document.write( "\"+S%5B2%5D++=+6+=+%281%2F4%29%285%5E2+-+1%29+\"
\n" ); document.write( "Assume \"+S%5Bk%5D+=+1%2B5%2B5%5E2++\" + … + \"+5%5E%28k-1%29+\" = \"+%281%2F4%29%285%5Ek+-+1%29+\" is true for n=k.\r
\n" ); document.write( "\n" ); document.write( "Now we need to show that that assumption leads to \"+S%5Bk%2B1%5D+=+%281%2F4%29%285%5E%28k%2B1%29+-+1+%29+\" :\r
\n" ); document.write( "\n" ); document.write( "\"+S%5Bk%2B1%5D+=+1%2B5%2B5%5E2+\" + … + \"+5%5E%28k-1%29+%2B+5%5Ek+\"
\n" ); document.write( "On the right hand side, all but the last term are really just \"+S%5Bk%5D+\"
\n" ); document.write( "\"+S%5Bk%2B1%5D+=+S%5Bk%5D+%2B+5%5Ek+\"
\n" ); document.write( "\"+S%5Bk%2B1%5D+=+%281%2F4%29%285%5Ek+-+1%29+%2B+5%5Ek++\"
\n" ); document.write( "\"+S%5Bk%2B1%5D+=+%281%2F4%29%285%5Ek+-+1+%2B+4%2A5%5Ek%29+\"
\n" ); document.write( "\"+S%5Bk%2B1%5D+=+%281%2F4%29%285%2A5%5Ek+-+1%29+\"
\n" ); document.write( "\"+S%5Bk%2B1%5D+=+%281%2F4%29%285%5E%28k%2B1%29+-+1%29+\"
\n" ); document.write( " DONE.
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