SOLUTION: State which is greater without evaluating A or B: A=20000(1+2+3+...+20001) or B=20001(1+2+3+...+20000)

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Question 1094794: State which is greater without evaluating A or B:
A=20000(1+2+3+...+20001) or
B=20001(1+2+3+...+20000)
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
A = 20000*(1+2+3+...+20001) = 20000%2A%28%2820001%2A20002%29%2F2%29 = %281%2F2%29%2A20000%2A20001%2A20002.


B = 20001*(1+2+3+...+20000) = 20001%2A%28%2820000%2A20001%29%2F2%29 = %281%2F2%29%2A20000%2A20001%5E2.



Now, comparing these expressions, you may conclude (without evaluating) that  A > B.



HINT.  I used well known formula for the sum of the first "n" natural numbers


          1 + 2 + 3 + . . . + n = %28n%2A%28n%2B1%29%29%2F2.