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 functionint main(){ int n = 10; // Function call cout << sumOfSeries(n); return 0;} |
Java
// Java Program to// find sum of // series// 1 + 2 + 2 + 3 + // . . . + npublic 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 + # . . . + nimport 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 methodn = 10# Function callprint (sumOfSeries(n))# This code is contributed by Gitanjali |
C#
// C# Program to find sum of// series 1 + 2 + 2 + 3 + . . . + nusing 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 callecho(sumOfSeries($n));// This code is contributed by Ajit.?> |
Javascript
<script>// Javascript Program to// find sum of // series// 1 + 2 + 2 + 3 + // . . . + n // Function that find // sum of series. function sumOfSeries( n) { let sum = 0; for (let i = 1; i <= n; i++) for (let j = 1; j <= i; j++) sum = sum + i; return sum; } // Driver Code let n = 10; document.write(sumOfSeries(n));// This code contributed by Princi Singh</script> |
Output:
385
Time Complexity: O(n2)
Auxiliary Space: O(1)
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 + // . . . + npublic 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 + # . . . + nimport 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 methodn = 10# Function callprint (sumOfSeries(n))# This code is contributed by Gitanjali. |
C#
// C# Program to find sum of series// 1 + 2 + 2 + 3 + . . . + nusing 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 callecho(sumOfSeries($n));// This code is contributed by Ajit.?> |
Javascript
<script>// javascript Program to // find sum of series// 1 + 2 + 2 + 3 + // . . . + n // Function that find sum of series. function sumOfSeries(n) { var sum = 0; for (let i = 1; i <= n; i++) sum = sum + i * i; return sum; } // Driver Code var n = 10; document.write(sumOfSeries(n));// This code is contributed by Amit Katiyar</script> |
Output:
385
Time Complexity: O(n)
Auxiliary Space: O(1)
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 functionint main(){ int n = 10; // Function call cout << sumOfSeries(n); return 0;} |
Java
// Java Program to // find sum of series// 1 + 2 + 2 + 3 + // . . . + npublic 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 + # . . . + nimport math # Function that find# sum of series.def sumOfSeries( n): return ((n * (n + 1) * (2 * n + 1)) / 6)# Driver methodn = 10# Function callprint (sumOfSeries(n))# This code is contributed by Gitanjali |
C#
// C# Program to find sum of series// 1 + 2 + 2 + 3 + . . . + nusing 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 callecho(sumOfSeries($n));// This code is contributed by Ajit.?> |
Javascript
<script>// javascript Program to // find sum of series// 1 + 2 + 2 + 3 + // . . . + n// Function that find// sum of series.function sumOfSeries(n){ return (n * (n + 1) * (2 * n + 1)) / 6;}// Driver Codevar n = 10;document.write(sumOfSeries(n));// This code is contributed by Amit Katiyar </script> |
Output :
385
Time Complexity: O(1)
Auxiliary Space: O(1)
Please refer sum of squares of natural numbers for details of above formula and more optimizations.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
… [Trackback]
[…] Read More on on that Topic: geeksforgeeks.org/program-to-find-sum-of-series-1-2-2-3-3-3-n/ […]
… [Trackback]
[…] Information on that Topic: geeksforgeeks.org/program-to-find-sum-of-series-1-2-2-3-3-3-n/ […]