document.write( "Question 696784: write the geometric series -9/2 + 3/2 - 1/2 + 1/6 - .......... + 1/39366 in summation notation\r
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\n" ); document.write( "\n" ); document.write( "than \r
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\n" ); document.write( "\n" ); document.write( "using the formula for the sum of an geometric series, computer the sum in the problem above \r
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\n" ); document.write( "\n" ); document.write( "Macy Gunderson \n" ); document.write( "

Algebra.Com's Answer #429550 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the numbering of the terms be
\n" ); document.write( "1,2,3,4, . . . etc.
\n" ); document.write( "The changing sign part goes
\n" ); document.write( "term #1 is (-)
\n" ); document.write( "term #2 is (+)
\n" ); document.write( "term #3 is (-)
\n" ); document.write( "etc.
\n" ); document.write( "That part of the general formula is
\n" ); document.write( " $\"+%28-1%29%5En+\"$ where $\"+n+\"$ is the number of the term
\n" ); document.write( "------------
\n" ); document.write( "It looks like I might be able to have a $\"+1%2F2+\"$ in each
\n" ); document.write( "term, so i've got so far:
\n" ); document.write( " $\"+%281%2F2%29%2A%28-1%29%5En+\"$
\n" ); document.write( "But, obviously, that's not all of it.
\n" ); document.write( "What if I put in a factor of $\"+3%5E%28+3-n%29+\"$ ? Now I have
\n" ); document.write( " $\"+%281%2F2%29%2A%28+3%5E%283-n%29+%29%2A%28-1%29%5En+\"$
\n" ); document.write( "I'll test it out
\n" ); document.write( " $\"+n+=+1+\"$
\n" ); document.write( " $\"+%281%2F2%29%2A%28+3%5E%283-1%29%29%2A%28-1%291%5E1+=+%281%2F2%29%2A9%2A%28-1%29+\"$
\n" ); document.write( " $\"+-9%2F2+\"$
\n" ); document.write( "---------
\n" ); document.write( " $\"+n+=+2+\"$
\n" ); document.write( " $\"+%281%2F2%29%2A%28+3%5E%283-2%29%29%2A%28-1%291%5E2+=+%281%2F2%29%2A3%2A1+\"$
\n" ); document.write( " $\"+3%2F2+\"$
\n" ); document.write( "---------
\n" ); document.write( " $\"+n+=+3+\"$
\n" ); document.write( " $\"+%281%2F2%29%2A%28+3%5E%283-3%29%29%2A%28-1%291%5E3+=+%281%2F2%29%2A3%5E0%2A%28-1%29+\"$
\n" ); document.write( " $\"+-1%2F2+\"$
\n" ); document.write( "----------
\n" ); document.write( " $\"+n+=+4+\"$
\n" ); document.write( " $\"+%281%2F2%29%2A%28+3%5E%283-4%29%29%2A%28-1%291%5E4+=+%281%2F2%29%2A3%5E%28-1%29%2A1+\"$
\n" ); document.write( " $\"+1%2F6+\"$
\n" ); document.write( "This works
\n" ); document.write( "So the formula is
\n" ); document.write( " $\"+%281%2F2%29%2A%28+3%5E%283-n%29+%29%2A%28-1%29%5En+\"$
\n" ); document.write( "I'm not sure about the summation notation. Are they
\n" ); document.write( "looking for the sum of all the terms?
\n" ); document.write( "Us the sigma ( summation ) symbol in front
\n" ); document.write( "of what I just gave you.\r
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