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
2 answers
The sum of the series
a + ar + ar2 + ... is a/(1 - r) for |r| < 1
1 answer
one fourth the sum of r and ten is identical to r munus 4
1 answer
void main() { int num,r,sum=0; clrscr(); printf("enter the number\n"); scanf("%d",&num); while(num!=0) { r=num%10; sum=sum+r; num=num/10 } printf("The sum of individual digit of given number is=%d",sum); getch() }
1 answer
For an Arithmetic Progression,
Sum = 15[a + 7d].{a = first term and d = common difference}
For a Geometric Progression,
Sum = a[1-r^15]/(r-1).{r = common ratio }.
1 answer
The formula for the sum of the series r(1/n2-1/n2) is r(1-1/n2).
1 answer
1 answer
#include<stdio.h>
#define PIE 3.142
void main()
{
int r,sum;
printf("Enter the radius of area\n");
scanf("%d",&r);
sum=PIE*r*r;
printf("The area of circle is:%d",sum);
}
1 answer
this is actually an equation
let the 'sum' be x
we are assuming r means are meaning =
so
x/6 = 7
x=42
so thats the answer
2 answers
Could be (r + 8)/2 or r/2 + 4
1 answer
Erm..they r and there not coz some r natural and sum r coz of humans
1 answer
the sum of p and r is p + r
5 times this sum is 5 × (p + r) = 5(p + r)
Multiplication is not written as it looks like an 'x' - it is implied by two things next to each other.
The brackets are needed as the addition needs to be done before the multiplication.
1 answer
#include
int main()
{
int num, r, sum=0, temp;
print f("enter a number:");
scan f("%d",&num);
temp=num;
while(n!=0)
{
r=num%10;
num=num/10;
sum=sum*10+r;
}
if(temp==sum)
print f("%d is a palindrome",temp);
else
print f("%d is not a palindrome",temp);
return 0;
}
1 answer
(r+5)(r-4)
The idea is to get two numbers whose product in this case is -20, and whose sum in this case s +1.
1 answer
Suppose the first term is a, the second is a+r and the nth is a+(n-1)r.
Then the sum of the first five = 5a + 10r = 85
and the sum of the first six = 6a + 15r = 123
Solving these simultaneous equations, a = 3 and r = 7
So the first four terms are: 3, 10, 17 and 24
1 answer
/*This program takes a square matrix from user and check whether it's a Magic Square or not. */
#include<stdio.h>
#include<conio.h>
int num[10][10],sum[21],r,c,i=0,x;
void read_matrix()
{ for(r=0;r<x;r++)
{ for(c=0;c<x;c++)
{ printf("Enter the value of matrix[%d][%d] :",r,c);
scanf("%d",&num[r][c]);
}
}
}
void calculate_sum()
{ int sum_row,sum_col=0,ctr=0;
for(r=0;r<x;r++)
{ sum_row = 0;
for(c=0;c<x;c++)
{ printf("\t%d",num[r][c]);
sum_row = sum_row + num[r][c];
}
sum[ctr] = sum_row;
ctr++;
printf(":: %d",sum_row);
printf("\n");
}
while(i<x)
{ printf("\t::");
i++;
}
printf("\n");
for(c=0;c<x;c++)
{sum_col = 0;
for(r=0;r<x;r++)
sum_col = sum_col + num[r][c];
sum[ctr] = sum_col;
ctr++;
printf("\t%d",sum_col);
}
for(r=0,c=0;r<x;r++,c++)
sum[2*x] = sum[2*x] + num[r][c];
for(r=0,c=x-1;r<x;r++,c--)
sum[2*x+1] = sum[2*x+1] + num[r][c];
}
char check_matrix()
{ char c;
for(i=0;i<2*x+1;i++)
{ if(sum[i] == sum[i+1])
c = 'Y';
else
{ c = 'N';
break;
}
}
return c;
}
void main()
{ char c;
clrscr();
printf("Enter d no. of rows or cols u want in your matrix :");
scanf("%d",&x);
read_matrix();
calculate_sum();
c = check_matrix();
if(c=='Y')
printf("\nThis matrix is a Magic Square");
else
printf("\nThis matrix is not a Magic Square");
getch();
}
1 answer
S.I. = (P x R x T)/100
where R is rate, T is time, P is Original sum and S.I. is simple interest.
800x100 = P x R x T
P = 80000/(5x7) = 80000/35 = 2285.71
So, the original sum is Rs 2285.71
1 answer
since you do not know what r and s is all you need to write is...
2r + 2s
the sum just simply means add them together.
1 answer
Suppose the nth term is = arn where n = 1,2,3, ...
Then the sum to the nth term is a*(rn+1 - 1)/(r - 1) or, equivalently,
a*(1 - rn+1)/(1 - r)
1 answer
In honey trees.U can c dat trees r green but sum of dem r yellow.Da yellow 1s r da honey trees.
1 answer
The sum to infinity of a geometric series is given by the formula S∞=a1/(1-r), where a1 is the first term in the series and r is found by dividing any term by the term immediately before it.
1 answer
It is the sum of:
1) Initial endowment (inheritance).
2) Life-time wages.
3) Sum of interest on wealth (e-r).
This can be represented mathematically in a form such as:
I = e-r[k0 + int(wAL(t))dt]
1 answer
Well, it's very hard to write a flowchart in text, so I'll give you some pseudo code instead.
int number = the given number
int sum = 0
loop while number is not 0
sum = sum + (number mod 10)
number = number / 10
6 answers
your nan minus your mum squared all dived by 2 to the sum of r=20 to r= 1.
1 answer
Let the three numbers in GP: a/r, a, ar---------(A)
Where '^' is power of . . .
Sum of these numbers are:
a/r +a +ar = 38
a(1\r+1+r) = 38 ---- (1)
Product of these numbers are:
a^3 = 1728
= (12)^3
a = 12
Putting the value of a in (1) you will get:
12(1\r+1+r) = 38
And factorising, we get
r = 2/3 or r = 3/2
Sub. the r and a value in (A), we get
8,12,18 or 18,12,8. When a = 12
And smallest no. is 8.
1 answer
NPV=NFV/(1+r)^n The role of the "(1+r)^n" is to discount the future money to what it is worth in todays dollars. The 1 accounts to the sum itself and the plus r takes into account the interest rate. NPV=NFV/(1+r)^n The role of the "(1+r)^n" is to discount the future money to what it is worth in todays dollars. The 1 accounts to the sum itself and the plus r takes into account the interest rate.
1 answer
The sum = 2r : where r is the row number.
1 answer
#include<stdio.h>
#include<conio.h>
main()
{
int n,s,r,t;
clrscr();
printf("enter n");
scanf("%d",&n);
s=0;t=0;
while(n!=0)
{
r=n%10;
{
if(r%2!=0)
t=t+r;
if(r%2==0)
s=s+r;
}
n=n/10;
}
printf("sum of even position digits%d\n",s);
printf("sum of odd position digits%d\n",t);
getch();
}
1 answer
The sum of a geometric sequence is a(1-rn)/(1-r)
In this case, a = 8, r = -2 and n=15
So the sum is 8(1-(-2)15)/(1+2)
=8(1+32768)/3
=87,384
So the sum of the first 15 terms of the sequence 8, -16, 32, -64.... is 87,384.
1 answer
I hav lots of friends sum of them r Frey,Yaz,Beth,Gab.......................
1 answer
why do you want to know r u gunna kill sum one
1 answer
.....5
.....Σ 9r
...r=1
1 answer