document.write( "Question 540972: Find the sum of the geometric series:
\n" ); document.write( "1+ sqrt6+ 6+...+7776 \n" ); document.write( "

Algebra.Com's Answer #353957 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Each term in the series is the previous one multiplied by $\"sqrt%286%29\"$ .
\n" ); document.write( "It is a geometric series.
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\n" ); document.write( "I multiplied by $\"%28%28sqrt%286%29%2B1%29%2F%28sqrt%286%29%2B1%29%29=1\"$ to rationalize (get rid of the square root in the denominator).
\n" ); document.write( "You may get to
\n" ); document.write( " $\"sum=%28%287776sqrt%286%29-1%29%2F%28sqrt%286%29-1%29%29\"$ from a carefully applied formula from your book, or (if allowed) deduce it from
\n" ); document.write( "sum*1=1+sqrt6+6+.....+7776, so
\n" ); document.write( "sum*sqrt6=sqrt6+6+6sqrt6+.....+7776*sqrt6, so subtracting
\n" ); document.write( "sum*sqrt6 - sum*1 = sum*(sqrt6-1)=7776*sqrt6-1
\n" ); document.write( "ALTERNATE WORK-UP
\n" ); document.write( " $\"7776=6%5E5\"$ We knew it had to be a power of 6.
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can be grouped as
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\n" ); document.write( "and the parentheses can be easily calculated as
\n" ); document.write( " $\"1%2B6%2B6%5E2%2B6%5E3%2B6%5E4%2B6%5E5=%286%5E6-1%29%2F%286-1%29=46655%2F5=9331\"$ and
\n" ); document.write( " $\"1%2B6%2B6%5E2%2B6%5E3%2B6%5E4=%286%5E5-1%29%2F%286-1%29=7775%2F5=1555\"$ \n" ); document.write( "

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