Because the series is ~ 0,3,-3,0,3,-3,0 .... Upto infinite .. Therefore we can imagine it as a set where the sum of every third is ZERO , so after every 3 terms we start from scratch with a zero... At A99 , the sum will be zero , and the 100th term will be a 0 , followed by the 101st term ie a 3 therfore from numbers 1 thru 99 the sum = 0 , from 100-101 the sum is 0+3 ie. 3. Therefore the answer is +3 ...

We an also devide the closest term to 101 by 3 , ie 99 so start with from a clean state from 99 , and just calculate the sum of 100 and 101st term... So the sum of the first two terms of the series ... That is S2 .. which is 0 +3 = 3 ...

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