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Question

Make generalised formula for this

1+2+3+ till.....+99+100 = ______


Solution

1 + 2 + 3 + . . . . + 99 + 100 = ? But we should rearranged the numbers to add them like this: (1 + 100) + (2 + 99) + (3 + 98) + . . . . + (50 + 51) = ? If you notice every pair of numbers adds up to 101. There are 50 pairs of numbers, so the answer is 50*101 = 5050. In general to find the sum of all the numbers from 1 to N: 1 + 2 + 3 + 4 + . . . . + N = (1 + N)*(N/2) That is "1 + N quantity times N divided by 2."

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