document.write( "Question 259364: what is the sum of the first 1,000 consecutive odd numbers? \n" ); document.write( "
Algebra.Com's Answer #190956 by CharlesG2(834)\"\" \"About 
You can put this solution on YOUR website!
what is the sum of the first 1,000 consecutive odd numbers?\r
\n" ); document.write( "\n" ); document.write( "consecutive numbers both even and odd table
\n" ); document.write( "\"+sum%28+i%2C1%2Cn+%29+=+%28n%28n%2B1%29%29%2F2+\"
\n" ); document.write( "(the sigma sign you see means to sum from n=0 to n=n)
\n" ); document.write( "n n(n+1)/2
\n" ); document.write( "1 1
\n" ); document.write( "2 3
\n" ); document.write( "3 6
\n" ); document.write( "4 10
\n" ); document.write( "5 15
\n" ); document.write( "10 55
\n" ); document.write( "100 5050
\n" ); document.write( "1000 500500
\n" ); document.write( "2000 2001000\r
\n" ); document.write( "\n" ); document.write( "now what is an odd number? an odd number can not be divisible by 2, we need to come up with a formula that only comes up with an odd number\r
\n" ); document.write( "\n" ); document.write( "2n-1 is an odd number where n=1,2,3,4,...
\n" ); document.write( "n=1 ---> 2n-1=2-1=1
\n" ); document.write( "n=2 ---> 2n-1=4-1=3
\n" ); document.write( "n=3 ---> 2n-1=6-1=5
\n" ); document.write( "n=4 ---> 2n-1=8-1=7
\n" ); document.write( "and so on to...
\n" ); document.write( "n=1000 --->2n-1=2000-1=1999\r
\n" ); document.write( "\n" ); document.write( "we want to sum the first 1000 consecutive odd numbers though
\n" ); document.write( "1+3=4=2^2
\n" ); document.write( "4+5=9=3^2
\n" ); document.write( "9+7=16=4^2
\n" ); document.write( "16+9=25=5^2
\n" ); document.write( "see what is happening here?\r
\n" ); document.write( "\n" ); document.write( "\"+sum%28+i%2C1%2C2n-1+%29+=+n%5E2+\"
\n" ); document.write( "n 2n-1
\n" ); document.write( "1 1
\n" ); document.write( "2 3
\n" ); document.write( "3 5
\n" ); document.write( "4 7
\n" ); document.write( "5 9
\n" ); document.write( "10 19
\n" ); document.write( "100 199
\n" ); document.write( "1000 1999\r
\n" ); document.write( "\n" ); document.write( "n^2 plug in 1000 for n
\n" ); document.write( "1000^2=1000000 or 1 million\r
\n" ); document.write( "\n" ); document.write( "the sum of the first 1,000 consecutive odd numbers is 1 million\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );