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What is the sum of 1 and 1?
The sum of 1 and 1 is 2.
What is the sum of all the positive proper fractions with denominators less than or equal to 100?
Consider a denominator of r; It has proper fractions: 1/r, 2/r, ...., (r-1)/r Their sum is: (1 + 2 + ... + (r-1))/r The numerator of this sum is 1 + 2 + ... + (r-1) Which is an Arithmetic Progression (AP) with r-1 terms, and sum: sum = number_of_term(first + last)/2 = (r-1)(1 + r-1)/2 = (r-1)r/2 So the sum of the proper fractions with a denominator or r is: sum{r} = ((r-1)r/2)/r = ((r-1)r/2r = (r-1)/2 Now consider the sum of the proper fractions with a denominator r+1: sum{r+1} = (((r+1)-1)/2 = ((r-1)+1)/2 = (r-1)/2 + 1/2 = sum{r) + 1/2 So the sums of the proper fractions of the denominators forms an AP with a common difference of 1/2 The first denominator possible is r = 2 with sum (2-1)/2 = ½; The last denominator required is r = 100 with sum (100-1)/2 = 99/2 = 49½; And there are 100 - 2 + 1 = 99 terms to sum So the required sum is: sum = ½ + 1 + 1½ + ... + 49½ = 99(½ + 49½)/2 = 99 × 50/2 = 2475
What is the sum of the digits of the number 11?
1 + 1 = 2 The sum of the digits is therefore 2.
Can the sum of two mixed numbers equal 2?
Only if you include negatives. The sum of 3 and 1/2 + -1 and 1/2 equals 2.
What is an equation to find the sum of all the integers from 1 to 2010?
To calculate the sum of the numbers 1 to n, the formula is: sum = n(1 + n) / 2 So, an equation to find the sum of the integers 1 to 2010 is: sum = 2010 x (1 + 2010) / 2
