SOLUTION: Find the sum of all positive even integers from 1-100

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Question 980120: Find the sum of all positive even integers from 1-100
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the sum of all positive even integers from 1-100
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There are 50 of them from 2 to 100
--> 25 pairs
2 + 100 = 102
4 + 98 = 102
6 + 96 = 102
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25 pairs * 102 = 2550

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if an even number is N, then we have
N+=+%28First_+Even+%2B+Last+_Even%29%2F2+-+1
N+=+%282%2B100%29%2F2+-+1+=+50; so, there is 50 even numbers from 1 to 100
Sum+=+%28number_+of_+integers%29+%2A+%28average_+of_+biggest_+and_+smallest%29
biggest even number is 100, smallest is 2, so average of biggest and smallest even number is %28100%2B2%29%2F2=51
then, the sum of first 50 positive even integers is %2850%29%2851%29+=+2550+