How does Gauss add 1 to 100?


How does Gauss add 1 to 100?

Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you “fold” the series of numbers in the middle and add them in pairs—1 + 100, 2 + 99, 3 + 98, and so on—all the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50×101.

What is Gauss’s formula?

Gauss added the rows pairwise – each pair adds up to n+1 and there are n pairs, so the sum of the rows is also ntimes (n+1). It follows that 2times (1+2+ldots +n) = ntimes (n+1), from which we obtain the formula. Gauss’ formula is a result of counting a quantity in a clever way.

How many 9s are there in 100?

Between 1 and 100, the digit 9 occurs in 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 and 99. ∴ The digit occurs 20 times between 1 and 100.

What is the total number of digits from 1to100?

→ Total number of digits from 1 to 100 are = 9 + 90 * 2 + 3 = 9 + 180 + 3 = 192 digits (Ans.) therefore, the total number of digits from 1 to 100 are 192 .

What did Gauss do for math?

Gauss is generally regarded as one of the greatest mathematicians of all time for his contributions to number theory, geometry, probability theory, geodesy, planetary astronomy, the theory of functions, and potential theory (including electromagnetism).

What do you get if you multiply all the numbers on your phone’s keypad?

The answer to What number do you get when you multiply all of the numbers on a telephone’s number pad? Riddle is “Zero (0).”

How many numbers are there from 421to 430?

Step-by-step explanation: if you consider it in the reasoning way then you can consider 30 . At the same time if you consider it as simple math then 10 is right!!

What is the sum of all odd numbers from 1 to 100?

The sum of odd numbers 1 to 100 is 2500. The average or mean of all odd numbers 1 to 100 is 50.

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