2014 UNCO Math Contest II Problems/Problem 2
Define the Cheshire Cat function by
Find the sum
It is evident that we are being asked to find the sum of the sequence .
A straight-forward approach is to find the sum of all the odd numbers from 1 to 289, inclusive, and subtract the sum of all the even numbers from 2 to 288, inclusive. Doing so would give you .
However, a faster method would be to see that you can group the terms in the sequence into . Using this, we can reduce many pairs of positive and negative numbers to s. Since there are as many s as there are odd numbers between 1 and 289, inclusive, and there are 145 odd numbers, the answer is .
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