SOLUTION: without computing each sum find which is greater o or e and by how much o = 5+7+9+11+..+105. E = 4+6+8+10+...+104

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Question 1163476: without computing each sum find which is greater o or e and by how much o = 5+7+9+11+..+105. E = 4+6+8+10+...+104
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


In each sum there are exactly the same number of terms, namely 101 terms. Each term in sum O is one larger than the corresponding term in sum E. That should be enough information for you to answer the question on your own.


John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

Without computing, it is clear that the number of addends is the same in both sums.


From the other side, each addend in the first sum is 1 unit greater than the corresponding addend in the second sum.


It leads us to the conclusion that the O-value is greater than E-value.



Next, O-value is greater than E-value exactly by the number of addends in each sum.


The number of intervals of the length 2 between  4 and 104 inclusive is   =  = 50.


Hence the number of terms in each sum is 50+1 = 51.


Thus O-value is 51 units greater than E-value.

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