SOLUTION: What is the difference between the sum of all postive odd integers less than 102 and the sum of all positive even integers less than 102 ?

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Question 701144: What is the difference between the sum of all postive odd integers less than 102 and the sum of all positive even integers less than 102 ?
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
What is the difference between the sum of all postive odd integers less than 102 and the sum of all positive even integers less than 102 ?
==========
--> 1 to 101
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The sum of 51 odd numbers = 51^2 = 2601
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The sum of all numbers from 1 to 101 = 5151
--------
Evens = 5151 - 2601 = 2550
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
 
The other tutor's answer is incorrect.  

The first 101 integers consist of 50 even numbers and 51 odd numbers

sum of odds  = 1 + 3 + 5 + 7 + ··· + 95 + 97 + 99 + 101
sum of evens =     2 + 4 + 6 + ··· + 94 + 96 + 98 + 100
-------------------------------------------------------
difference   = 1 + 1 + 1 + 1 + ··· +  1 +  1 +  1 +   1

When we subtracted them above, term by term, there is a 1 
in each of the positions of the 51 odd numbers. The sum of 
51 1's is 51.

Answer: 51

Edwin
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