document.write( "Question 788794: How many terms of the series 2 + 2√2 + 4 .....will amount to 30 + 14√2 \n" ); document.write( "
Algebra.Com's Answer #478607 by Edwin McCravy(20054)\"\" \"About 
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document.write( "2 + 2√2 + 4\r\n" );
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document.write( "That's a geometric series with common ratio r = √2 \r\n" );
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document.write( "Geometric sequence:\r\n" );
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document.write( "Sn = \"a%5B1%5D%281-r%5En%29%2F%281-r%29\"\r\n" );
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document.write( "Sn = \"a%5B1%5D%281-r%5En%29%2F%281-r%29\" \r\n" );
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document.write( "30 + 14√2 = \"2%281-%28sqrt%282%29%29%5En%29%2F%281-sqrt%282%29%29\"\r\n" );
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document.write( "(30 + 14√2)(1 - √2) = 2·[1 - (√2)n\r\n" );
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document.write( "30 - 16√2 - 14·2 = 2 - 2(√2)n\r\n" );
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document.write( "Divide every term by 2\r\n" );
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document.write( "15 - 8√2 - 14 = 1 - (√2)n\r\n" );
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document.write( "1 - 8√2 = 1 - (√2)n\r\n" );
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document.write( "-8√2 = -(√2)n\r\n" );
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document.write( "8√2 = (√2)n\r\n" );
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document.write( "Write 8 as 23 and √2 as 2.5\r\n" );
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document.write( "232.5 = (2.5)n\r\n" );
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document.write( "23.5 = 2.5n\r\n" );
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document.write( "Equate the powers of 2\r\n" );
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document.write( "3.5 = .5n\r\n" );
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document.write( "\"3.5%2F.5\" = n\r\n" );
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document.write( "7 = n\r\n" );
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document.write( "Answer: It will take 7 terms for the sum to amount to 30 + 14√2   \r\n" );
document.write( "Edwin
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