document.write( "Question 1018961: Prove that: $\"sum%28%282k-1%5E%22%22%29%5E%22%22%5E%22%22%5E%22%22%2Ck=1%2Cn%29\"$ $\"%22%22=%22%22\"$ $\"sum%28+%28%28n%5E2-1%29%2Fn%5E2%29%5E%28k-1%29%2Ck=1%2Cinfinity%29\"$ \n" ); document.write( "

Algebra.Com's Answer #635723 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Prove that:
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document.write( "The left side is the sum of the arithmetic series:\r\n" );
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document.write( "1 + 3 + 5 + ... + 2n-1\r\n" );
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document.write( "The formula for this sum is\r\n" );
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document.write( "where a₁ = 1 and a_n = 2n-1 \r\n" );
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document.write( "--------\r\n" );
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document.write( "Now we see if we can show that the right side is also \r\n" );
document.write( "equal to n².\r\n" );
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document.write( "The right side is the sum of an infinite geometric series\r\n" );
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document.write( "The formula for this sum is \r\n" );
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document.write( "where a₁ = 1 and  \r\n" );
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document.write( "So the right side also equals n². \r\n" );
document.write( "That proves they are equal.\r\n" );
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document.write( "Edwin

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