SOLUTION: find the sum of the whole number from 1 to 9999

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Question 643622: find the sum of the whole number from 1 to 9999
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First do a shorter sequence to get the
right method. First find the sum of
0 to 10
+0+%2B+1+%2B+2+%2B+3+%2B+4+%2B+5+%2B+6+%2B+7+%2B+8+%2B+9+%2B+10+=+55+
( I did it on my calculator )
This is +%2810%2F2%29%2A%28+10+%2B+1+%29+
How about
+0+%2B+1+%2B+2+%2B+3+%2B+4+%2B+5+%2B+6+%2B+7+%2B+8+%2B+9+%2B+10+%2B+11+%2B+12+%2B+13+=+91+
This is +%2813%2F2%29%2A%28+13+%2B+1+%29+
----------------------
So, the formula is:
The sum of the numbers from 1 to n =
+%28n%2F2%29%2A%28+n+%2B+1+%29+
---------------
+n+=+9999+
+%28+9999%2F2+%29%2A%28+9999+%2B+1+%29+=+4999.5%2A10000+
+4999.5%2A10000+=+49995000+

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

You don't need a formula.

Suppose the sum = N, then

 N =     1 +     2 +     3 +     4 + ··· +  9996 +  9997 +  9998 +  9999

N also equals that same sum with the numbers added in the reverse order:

 N =  9999 +  9998 +  9997 +  9996 + ··· +     4 +     3 +     2 +     1


Now let's write those two equations one under the other, and add equals 
to equals term by term:

 N =     1 +     2 +     3 +     4 + ··· +  9996 +  9997 +  9998 +  9999
 N =  9999 +  9998 +  9997 +  9996 + ··· +     4 +     3 +     2 +     1
------------------------------------------------------------------------
2N = 10000 + 10000 + 10000 + 10000 + ··· + 10000 + 10000 + 10000 + 10000

Since we know there are 9999 terms on the right, that sum on the right is 
9999 times 10000 or 99990000, so that equation bercomes

2N = 99990000

Dividing both sides by 2

 N = 49995000 

Edwin