document.write( "Question 1039512: find the sum of even integers between 1 and 101 in a arithmetic sequence \n" ); document.write( "

Algebra.Com's Answer #654273 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The sum of ALL the integers from 1 to n
\n" ); document.write( "is given by:
\n" ); document.write( " $\"+S+=+%28+n%2A%28+n%2B1+%29%29+%2F+2+\"$
\n" ); document.write( "If $\"+n+=+101+\"$ ,
\n" ); document.write( " $\"+S+=+%28+101%2A102+%29+%2F+2+\"$
\n" ); document.write( " $\"+S+=+10302%2F2+=+5151+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "The sum of the ODD integers from 1 to n?
\n" ); document.write( "I notice that
\n" ); document.write( " $\"+1+=+1+\"$
\n" ); document.write( " $\"+1+%2B+3+=+4+\"$
\n" ); document.write( " $\"+1+%2B+3+%2B+5+=+9+\"$
\n" ); document.write( " $\"+1+%2B+3+%2B+5+%2B+7+=+16+\"$
\n" ); document.write( "Let $\"+k+\"$ = the number of odd integers from 1 to n
\n" ); document.write( "So, $\"+S%5Bodd%5D+=+k%5E2+\"$
\n" ); document.write( "The are $\"+51+\"$ odd integers in 1 - 101 sequence
\n" ); document.write( " $\"+k%5E2+=+51%5E2+\"$
\n" ); document.write( " $\"+S%5Bodd%5D+=+2601+\"$
\n" ); document.write( "-------------------
\n" ); document.write( " $\"+S%5Beven%5D+=+S+-+S%5Bodd%5D+\"$
\n" ); document.write( " $\"+S%5Beven%5D+=+5151+-+2601+\"$
\n" ); document.write( " $\"+S%5Beven%5D+=+2550+\"$
\n" ); document.write( "Hope I got it! \n" ); document.write( "

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