document.write( "Question 1164031: Calculate each of the following. Your answer must be a number. No arithmetic operations are allowed in your answer. Please give 7 places after your decimal point if you use scientific notation.
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Algebra.Com's Answer #788406 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Ikleyn hasn't noticed that 940! and 910! have over 2000 digits each and that\r\n" );
document.write( "is beyond the capacity of all calculators.  \r\n" );
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document.write( "a) \"940%21%2F%2830%21+910%21%29\"\r\n" );
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document.write( "\"X\"\"%22%22=%22%22\"\"940%21%2F%2830%21910%21%29\"\r\n" );
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document.write( "Take logs (base ten)\r\n" );
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document.write( "\"log%28X%29\"\"%22%22=%22%22\"\"log%28%28940%21%2F%2830%21910%21%29%29%29\"\r\n" );
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document.write( "\"log%28X%29\"\"%22%22=%22%22\"\"log%28940%21%29-log%2830%21%29-log%28910%21%29\"\r\n" );
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document.write( "We use Gosper's improvement of Stirling's approximate formula for n!:\r\n" );
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document.write( "n! = √[(2n+1/3)∙π]∙nn∙e-n\r\n" );
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document.write( "We take the log10 of that:\r\n" );
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document.write( "log(n!) = 0.5∙log[(2n+1/3)∙π]+n∙log(n)+(-n)/log(e)\r\n" );
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document.write( "We find by calculator using the above formula:\r\n" );
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document.write( "\"log%28940%21%29\"\"%22%22=%22%22\"\"2388.3890617535\" \r\n" );
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document.write( "\"log%28910%21%29\"\"%22%22=%22%22\"\"2299.3983388775\"\r\n" );
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document.write( "\"log%2830%21%29\"\"%22%22=%22%22\"\"32.42366007\"\r\n" );
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document.write( "[We didn't need Gosper's formula for that last one, for it isn't too large\r\n" );
document.write( "for the calculator.]\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "\"log%28X%29\"\"%22%22=%22%22\"\"log%28940%21%29-log%2830%21%29-log%28910%21%29\"\r\n" );
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document.write( "\"log%28X%29\"\"%22%22=%22%22\"\"56.56706293\"\r\n" );
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document.write( "\"X\"\"%22%22=%22%22\"\"10%5E56.56706293\"\r\n" );
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document.write( "\"X\"\"%22%22=%22%22\"\"10%5E56%2A10%5E0.56706293\"\r\n" );
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document.write( "\"X\"\"%22%22=%22%22\"\"10%5E56%2A3.690310679\"\r\n" );
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document.write( "Answer:  3.6903107 × 1056\r\n" );
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document.write( "Do the others the same way.  Use logs base ten.  Use Gosper's approximation\r\n" );
document.write( "formula or whatever approximation formula your teacher told you to use.  \r\n" );
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document.write( "Edwin

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