document.write( "Question 1104110: Simplify + $\"+%28%283%5E2999%29%2F%283%5E3000%29%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #718847 by math_helper(2461) $\"\"$ $\"About$

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\n" ); document.write( " $\"+S%5B5%5D+=+4%2F3+%2B+3%5E4%2F3%5E5+=+4%2A3%5E4%2F3%5E5+%2B+3%5E4%2F3%5E5+=+5%2F3+\"$
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\n" ); document.write( " $\"+S%5Bn%5D+=+n%2F3+\"$ <Ч Assertion
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\n" ); document.write( "Proof of $\"+S%5Bn%5D+=+n%2F3+\"$ by inductionЕ\r
\n" ); document.write( "\n" ); document.write( "We already see it is true for n=3,4,5, assume it is true for n.
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\n" ); document.write( "\n" ); document.write( "ЧЧЧЧЧЧЧЧЧЧЧЧЧ
\n" ); document.write( " $\"+S%5B3000%5D+=+3000%2F3+=+highlight%281000%29+\"$ \r
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\n" ); document.write( "To the student:
\n" ); document.write( " $\"+S%5Bn%5D+\"$ = partial sum (S is often used for this purpose). I found the first few partial sums to see if there was a pattern. That allowed me to assert $\"S%5Bn%5D+=+n%2F3\"$ , then I proved that assertion by induction so I could safely use it to compute $\"+S%5B3000%5D+\"$ .
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