###### Asked in Math and ArithmeticAlgebra

Math and Arithmetic

Algebra

# What is one-sixth the sum of r and 7?

## Answer

###### Wiki User

###### October 05, 2012 4:48AM

(r+7)/6, assuming r is a variable.

## Related Questions

###### Asked in Math and Arithmetic

### 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

###### Asked in Math and Arithmetic

### Find the sum of all positive integers not greater than 10000 that are not divisible by 7?

Sum(not div by 7) = Sum(all) - Sum(div by 7)
Now the sum of an AP is
Sn = n/2 (first + last)
where n is the number of terms
Sum(All) = 10000/2 (1 + 10000) = 50005000
Sum(div by 7) = (9996/7)/2 (7 + 9996) = 1428/2 (10003) =
7142142
Sum(not div by 7) = Sum(all) - Sum(div by 7)
= 50005000 - 7142142
= 42 862 858

###### Asked in Java Programming

### Write a program to find sum of all integers greater than 100 and less than 200 that are divided by 7?

...
int sum = 0;
for (int i = 101; i <= 199; i++)
if (i % 7 == 0) sum += i;
...
...
int sum = 0;
for (int i = 101; i <= 199; i++)
if (i % 7 == 0) sum += i;
...
...
int sum = 0;
for (int i = 101; i <= 199; i++)
if (i % 7 == 0) sum += i;
...
...
int sum = 0;
for (int i = 101; i <= 199; i++)
if (i % 7 == 0) sum += i;
...

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