Question

Fill in the blanks with the most appropriate words given below within brackets (consecutive, series, tedious, pairs, summing)

In the 1780s a provincial German schoolmaster gave his class the ______assignment of ____ the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: I+2+3+ + 98 + 99 +100 5,050, The smart aleck was Carl Friedrich Gauss, who was not just a calculating prodigy who added up all those numbers in his head. He had a deeper insight. If you fold the____ of numbers in the middle and add them in pairs-1 + 100, 2+ 99, 3 + 98, and so on-all the _____sum to 101. There are 50 such pairs, and so the grand total is simply50x101. The more general formula, for a list of_____ numbers from through, is nin+1Y2​

Answer 1

Answer:

In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: I+2+3+ + 98 + 99 +100 5,050, The smart aleck was Carl Friedrich Gauss, who was not just a calculating prodigy who added up all those numbers in his head. He had a deeper insight. If you fold the pairs of numbers in the middle and add them in pairs-1 + 100, 2+ 99, 3 + 98, and so on-all the series sum to 101. There are 50 such pairs, and so the grand total is simply50x101. The more general formula, for a list of consecutive numbers from through, is nin+1Y2