Program to find sum of series 1 + 2 + 2 + 3 + 3 + 3 + . . . + n

30 Nov, 2021
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++
Java
Python3
C#
PHP
Javascript
// 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 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 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# 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// 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.?>
<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++
Java
Python3
C#
PHP
Javascript
// 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 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 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# 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// 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.?>
<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++
Java
Python3
C#
PHP
Javascript
// 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 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 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# 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 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.?>
<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. 
jit_t
vt_m
princi singh
amit143katiyar
souravmahato348
avtarkumar719
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