document.write( "Question 1118204: 10. Evaluate the following. Show your work using concepts from this unit.\r
\n" ); document.write( "\n" ); document.write( "a) 1 - 3 + 5 - 7 + 9 -11 + ... + 201 - 203\r
\n" ); document.write( "\n" ); document.write( "b) 300 - 299 + 298 - 297 + ... + 100 - 99 \n" ); document.write( "
Algebra.Com's Answer #733461 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!
I will show you how to do part(a). You should then be able to do part(b) using the same approach.\r
\n" ); document.write( "\n" ); document.write( " a) 1 - 3 + 5 - 7 + 9 -11 + ... + 201 - 203
\n" ); document.write( "For an arithmetic series of length n, the sum can be found from this:
\n" ); document.write( "\"+S%5Bn%5D+=+%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29+\" (*)
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\n" ); document.write( "\n" ); document.write( "Separate the + and - terms to get two series:\r
\n" ); document.write( "\n" ); document.write( "Sum = (1+5+9+…+201) - 3-7-11-…-203
\n" ); document.write( "Factor -1 from the ungrouped terms:
\n" ); document.write( "Sum = (1+5+9+…+201) - (3+7+11+…+203)
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\n" ); document.write( "\n" ); document.write( "Each of these has length 51 (201 = 50*4+1, that's 51 terms. Similarly, 203=50*4+3, so the 2nd series also has 51 terms).
\n" ); document.write( "Using (*):
\n" ); document.write( " \"+Sum++=+%2851%2F2%29%281%2B201%29+-+%2851%2F2%29%283%2B203%29+\"
\n" ); document.write( " \"+Sum+=+5151+-+5253+\"
\n" ); document.write( " \"+Sum+=+highlight%28+-+102+%29+\"\r
\n" ); document.write( "\n" ); document.write( "——————————————————————————————
\n" ); document.write( "EDIT 6/5 - Yes, pairing up the terms to get 51*(-2) is a very quick way to solve. Thanks tutor @ikleyn, and @greenestamps too.\r
\n" ); document.write( "\n" ); document.write( " ( I got as far as noticing -102 is multiple of 51 but didn't connect the dots, so to speak.)
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