Program to find sum of series 1 + 2 + 2 + 3 + 3 + 3 + . . . + n
Given a positive integer n and the task is to find sum of series 1 + 2 + 2 + 3 + 3 + 3 + . . . + n.
Examples:
Input : n = 5
Output : 55
= 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 +
4 + 5 + 5 + 5 + 5 + 5.
= 55
Input : n = 10
Output : 385
Addition method: In addition method sum all the elements one by one.
Below is the implementation of this approach.
C++
// Program to find // sum of series // 1 + 2 + 2 + 3 + // . . . + n #include <bits/stdc++.h> using namespace std; // Function that find // sum of series. int sumOfSeries(int n) { int sum = 0; for (int i = 1; i <= n; i++) for (int j = 1; j <= i; j++) sum = sum + i; return sum; } // Driver function int main() { int n = 10; // Function call cout << sumOfSeries(n); return 0; } |
Java
// Java Program to // find sum of // series // 1 + 2 + 2 + 3 + // . . . + n public class GfG{ // Function that find // sum of series. static int sumOfSeries(int n) { int sum = 0; for (int i = 1; i <= n; i++) for (int j = 1; j <= i; j++) sum = sum + i; return sum; } // Driver Code public static void main(String s[]) { int n = 10; System.out.println(sumOfSeries(n)); } } // This code is contributed by Gitanjali |
Python3
# Python3 Program to # find sum of series # 1 + 2 + 2 + 3 + # . . . + n import math # Function that find # sum of series. def sumOfSeries( n): sum = 0 for i in range(1, n+1): sum = sum + i * i return sum # Driver method n = 10 # Function call print (sumOfSeries(n)) # This code is contributed by Gitanjali |
C#
// C# Program to find sum of // series 1 + 2 + 2 + 3 + . . . + n using System; public class GfG { // Function that find // sum of series. static int sumOfSeries(int n) { int sum = 0; for (int i = 1; i <= n; i++) for (int j = 1; j <= i; j++) sum = sum + i; return sum; } // Driver Code public static void Main() { int n = 10; Console.Write(sumOfSeries(n)); } } // This code is contributed by vt_m. |
PHP
<?php // Program to find // sum of series // 1 + 2 + 2 + 3 + // . . . + n // Function that find // sum of series. function sumOfSeries($n) { $sum = 0; for ($i = 1; $i <= $n; $i++) for ($j = 1; $j <= $i; $j++) $sum = $sum + $i; return $sum; } // Driver Code $n = 10; // Function call echo(sumOfSeries($n)); // This code is contributed by Ajit. ?> |
Output:
385
Time Complexity: O(n2)
Multiplication method:In multiplication method every elements multiply by itself and then add them.
Input n = 10
sum = 1 + 2 + 2 + 3 + 3 + 3 + 4 + . . . + 10
= 1 + 2 * 2 + 3 * 3 + 4 * 4 + . . . + 10 * 10
= 1 + 4 + 9 + 16 + . . . + 100
= 385
C++
// Program to find // sum of series // 1 + 2 + 2 + 3 + // . . . + n #include <bits/stdc++.h> using namespace std; // Function to find // sum of series. int sumOfSeries(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum = sum + i * i; return sum; } // Driver function. int main() { int n = 10; // Function call cout << sumOfSeries(n); return 0; } |
Java
// Java Program to // find sum of series // 1 + 2 + 2 + 3 + // . . . + n public class GfG{ // Function that find sum of series. static int sumOfSeries(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum = sum + i * i; return sum; } // Driver Code public static void main(String args[]) { int n = 10; System.out.println(sumOfSeries(n)); } } // This code is contributed by Gitanjali |
Python3
# Python3 Program to # find sum of series # 1 + 2 + 2 + 3 + # . . . + n import math # Function that find # sum of series. def sumOfSeries( n): sum = 0 for i in range(1, n+1): sum = sum + i * i return sum # Driver method n = 10# Function call print (sumOfSeries(n)) # This code is contributed by Gitanjali. |
C#
// C# Program to find sum of series // 1 + 2 + 2 + 3 + . . . + n using System; class GfG { // Function that find sum of series. static int sumOfSeries(int n) { int sum = 0; for (int i = 1; i <= n; i++) sum = sum + i * i; return sum; } // Driver Code public static void Main() { int n = 10; Console.WriteLine(sumOfSeries(n)); } } // This code is contributed by anuj_67. |
PHP
<?php // Program to find // sum of series // 1 + 2 + 2 + 3 + // . . . + n // Function to find // sum of series. function sumOfSeries($n) { $sum = 0; for ($i = 1; $i <= $n; $i++) $sum = $sum + $i * $i; return $sum; } // Driver Code $n = 10; // Function call echo(sumOfSeries($n)); // This code is contributed by Ajit. ?> |
Output:
385
Time Complexity: O(n)
Using formula: We also use formula to find the sum of series.
Input n = 10;
Sum of series = (n * (n + 1) * (2 * n + 1)) / 6
put n = 10 in the above formula
sum = (10 * (10 + 1) * (2 * 10 + 1)) / 6
= (10 * 11 * 21) / 6
= 385
C++
// C++ Program to // find sum of series // 1 + 2 + 2 + 3 + // . . . + n #include <bits/stdc++.h> using namespace std; // Function to find // sum of series. int sumOfSeries(int n) { return (n * (n + 1) * (2 * n + 1)) / 6; } // Driver function int main() { int n = 10; // Function call cout << sumOfSeries(n); return 0; } |
Java
// Java Program to // find sum of series // 1 + 2 + 2 + 3 + // . . . + n public class GfG { // Function that find // sum of series. static int sumOfSeries(int n) { return (n * (n + 1) * (2 * n + 1)) / 6; } // Driver Code public static void main(String s[]) { int n = 10; System.out.println(sumOfSeries(n)); } } // This code is contributed by 'Gitanjali'. |
Python3
# Python3 Program to # find sum of series # 1 + 2 + 2 + 3 + # . . . + n import math # Function that find # sum of series. def sumOfSeries( n): return ((n * (n + 1) * (2 * n + 1)) / 6) # Driver method n = 10 # Function call print (sumOfSeries(n)) # This code is contributed by Gitanjali |
C#
// C# Program to find sum of series // 1 + 2 + 2 + 3 + . . . + n using System; public class GfG { // Function that find // sum of series. static int sumOfSeries(int n) { return (n * (n + 1) * (2 * n + 1)) / 6; } // Driver Code public static void Main() { int n = 10; Console.WriteLine(sumOfSeries(n)); } } // This code is contributed by 'vt_m'. |
PHP
<?php // PHP Program to // find sum of series // 1 + 2 + 2 + 3 + // . . . + n // Function to find // sum of series. function sumOfSeries($n) { return ($n * ($n + 1) * (2 * $n + 1)) / 6; } // Driver Code $n = 10; // Function call echo(sumOfSeries($n)); // This code is contributed by Ajit. ?> |
Output :
385
Time Complexity: O(1)
Please refer sum of squares of natural numbers for details of above formula and more optiimizations.
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