 Let us look now at the strategy organizing data. Sometimes simply by neatly and cleverly organizing the data, you gain valuable insight to lead you in the right direction to solve a problem. Consider the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, and so on, how many terms are needed in order for the sum of the reciprocals of this sequence to equal 100. Let us begin by writing out the sum that we want. We are organizing the data in the way that the problem suggests. Now we see that the sum of these 2 terms is 1, the sum of these 3 terms is 1, the sum of these 3 is 1, so the last term in this sequence, since we are adding many ones, the last term must be 1 over 100, 100 times, this is the last set of terms. Now notice that this is as 1 term, 2 terms, 3 terms, 4 terms, we are concerned with the number of terms needed for the sum of the reciprocals to be equal to 100. And then this one is 100. This problem then boils down to simply adding the integers 1 through 100, which we can easily do, 51 plus 98 plus 99 plus 100. We notice that 1 plus 100 is equal to 101 and 2 and 99, the sum of them is also 101, the sum of 98 and 3 is also 101, and the sum of 50 and 51 is also 101. So we have 50 such pairs, so the answer must be 50 times 101, which is 5050, that is the number of terms needed for this sequence to be equal to 100. Certainly we could have used the formula for adding integers 1 through n, which was known to the Pythagorean more than 500 years before the Christian era. If we would have used the formula, we would have put 100 times 101 divided by 2, which is equal to 50 times 101, which is exactly our answer. Thank you.