document.write( "Question 643622: find the sum of the whole number from 1 to 9999 \n" ); document.write( "
Algebra.Com's Answer #404566 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "\r\n" ); document.write( "You don't need a formula.\r\n" ); document.write( "\r\n" ); document.write( "Suppose the sum = N, then\r\n" ); document.write( "\r\n" ); document.write( " N = 1 + 2 + 3 + 4 + ··· + 9996 + 9997 + 9998 + 9999\r\n" ); document.write( "\r\n" ); document.write( "N also equals that same sum with the numbers added in the reverse order:\r\n" ); document.write( "\r\n" ); document.write( " N = 9999 + 9998 + 9997 + 9996 + ··· + 4 + 3 + 2 + 1\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Now let's write those two equations one under the other, and add equals \r\n" ); document.write( "to equals term by term:\r\n" ); document.write( "\r\n" ); document.write( " N = 1 + 2 + 3 + 4 + ··· + 9996 + 9997 + 9998 + 9999\r\n" ); document.write( " N = 9999 + 9998 + 9997 + 9996 + ··· + 4 + 3 + 2 + 1\r\n" ); document.write( "------------------------------------------------------------------------\r\n" ); document.write( "2N = 10000 + 10000 + 10000 + 10000 + ··· + 10000 + 10000 + 10000 + 10000\r\n" ); document.write( "\r\n" ); document.write( "Since we know there are 9999 terms on the right, that sum on the right is \r\n" ); document.write( "9999 times 10000 or 99990000, so that equation bercomes\r\n" ); document.write( "\r\n" ); document.write( "2N = 99990000\r\n" ); document.write( "\r\n" ); document.write( "Dividing both sides by 2\r\n" ); document.write( "\r\n" ); document.write( " N = 49995000 \r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |