8546. Find the sum

For the given value of n, compute the sum

S =

Input. One positive integer n (n ≤ 1000).

Output. Print the sum with 6 decimal places.

Sample input 1	Sample output 1
5	0.833333
Sample input 2	Sample output 2
12	0.923077

SOLUTION

loops

Algorithm analysis

Compute the specified sum using a loop.

Let’s calculate the specified sum mathematically:

= =

Now we can use this formula to find the answer.

Algorithm implementation

Read the input value of n.

scanf("%d",&n);

In the variable i, iterate through the numbers 1, 2, 3, … n. On each iteration, add the value of 1 / (i * (i + 1)) to the resulting sum s.

s = 0; i = 1;

while(i <= n)

{

s += 1.0 / i / (i+1);

i++;

}

Print the answer.

printf("%lf\n",s);

Algorithm implementation– for loop

Read the input value of n.

scanf("%d",&n);

Compute the desired sum in the variable s.

s = 0;

Using a for loop, compute the sum of n terms. The i-th term is equal to 1 / (i * (i + 1)).

for (i = 1; i <= n; i++)

s += 1.0 / (i * (i+1));

Print the answer.

printf("%.6lf\n",s);

Algorithm implementation– formula

Read the input value of n.

scanf("%d", &n);

Compute the answer using the formula and print it.

s = 1 - 1.0 / (n + 1);

printf("%.6lf\n", s);

Java implementation

import java.util.*;

class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

int n = con.nextInt();

double s = 0;

for(int i = 1; i <= n; i++)

s += 1.0 / (i * (i+1));

System.out.printf("%6f\n", s);

con.close();

}

}

Python implementation

Read the input value of n.

n = int(input())

Compute the desired sum in the variable s.

s = 0;

Using a for loop, compute the sum of n terms. The i-th term is equal to 1 / (i * (i + 1)).

for i in range(1, n+1):

s += 1.0 / (i * (i + 1));

Print the answer.

print(s)