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.
// 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 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 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# 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 // 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. ?> |
<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
// 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 + // . . . + 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 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# 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 // 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. ?> |
<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++ 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 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 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# 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 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. ?> |
<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 Code var 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.