document.write( "Question 937614: simplify 1-2+3-4+...+49-50+49-48+47-46+...+1.please help.thanks in advance \n" ); document.write( "

Algebra.Com's Answer #571140 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"1-2%2B3-4%2B%22...%22%2B49-50%2B49-48%2B47-46%2B%22...%22%2B1=highlight%280%29\"$
\n" ); document.write( "There is more than one way to get to that answer.
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\n" ); document.write( "If you are studying arithmetic sequences, you may be expected to split that sum into three sums of arithmetic sequences,
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, and
\n" ); document.write( " $\"sum%28+2i%2C+i=1%2C+i=25+%29=2%2B4%2B6%2B%22...%22%2B46%2B48%2B50=25%2A%282%2B50%29%2F2=650\"$ , or
\n" ); document.write( " $\"sum%28+2i%2C+i=1%2C+i=24%29=2%2B4%2B6%2B%22...%22%2B46%2B48=24%2A%282%2B48%29%2F2=600\"$ ,
\n" ); document.write( "and calculate it as
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, or
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.
\n" ); document.write( "If you are not studying arithmetic sequences, it is easier to calculate it as
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,
\n" ); document.write( "or something like that.
\n" ); document.write( "You can see that the first bracket is a sum of $\"25\"$ terms of the form $\"2i-1-2i=-1\"$ for $\"i=1\"$ to $\"i=25\"$ ,
\n" ); document.write( "and that the second bracket is a sum of $\"24\"$ terms of the form $\"2i-%282i-1%29=1\"$ for $\"i=1\"$ to $\"i=24\"$ . \n" ); document.write( "

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