Algebra.Com's Answer #818449 by ikleyn(52915)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "You are running a foundation for street children. Mr. Park, a rich benefactor, offers two options for his donations :
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document.write( "OPTION A: To give $ 1,000 on day 1, $999 on day 2, $998 on day 3, with the process to end after 1,000 days.
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document.write( "OPTION B: To give $1 on day 1, $2 on day 2, $4 on day 3, for 19 days.
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document.write( "You have to tell him today which option you want to take.
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document.write( "OPTION (A) : You need to find the sum of the first 1000 natural numbers\r\n" );
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document.write( "  = 1000 + 999 + 998 + . . . + 2 + 1.\r\n" );
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document.write( " In your high school, you diligently learned about arithmetic progression, and you know\r\n" );
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document.write( " that the sum of the first n natural numbers is  .\r\n" );
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document.write( " So, you have a happy opportunity to apply your knowledge, and you quickly calculate\r\n" );
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document.write( " =  = 500*1001 = 500500 dollars.\r\n" );
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document.write( "OPTION (B) : You need to find the sum of the first 19 terms of the geometric progression\r\n" );
document.write( " with the first term of 1 and the common ratio of 2.\r\n" );
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document.write( "  =  +  +  + . . .  .\r\n" );
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document.write( " In your high school, you diligently learned about geometric progression, and you know\r\n" );
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document.write( " that the sum of the first n terms of the given progression is  .\r\n" );
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document.write( " So, you have a happy opportunity to apply your knowledge, and you quickly calculate\r\n" );
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document.write( " =  = 524287 dollars.\r\n" );
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document.write( "Now you have everything to make your decision and announce it to Mr. Park.\r\n" );
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document.write( "I am sure you will make a right decision, and the street children will be happy ( ! )\r
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document.write( "Solved.\r
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