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## Sum of the series 1 + (1+2) + (1+2+3) + (1+2+3+4) + …… + (1+2+3+4+…+n)

• Discuss
• Given the value of
n, we need to find the sum of the series where i-th term is sum of first i natural numbers.
Examples :

Input  : n = 5    Output : 35 Explanation : (1) + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) = 35  Input  : n = 10 Output : 220 Explanation : (1) + (1+2) + (1+2+3) +  .... +(1+2+3+4+.....+10) = 220

Naive Approach :
Below is implementation of above series :

## C++

#include <bits/stdc++.h>

using
namespace
std;

int
sumOfSeries(
int
n)

{

int
sum = 0;

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

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

sum += j;

return
sum;

}

int
main()

{

int
n = 10;

cout << sumOfSeries(n);

return
0;

}

## Java

import
java.util.*;

class
GFG {

static
int
sumOfSeries(
int
n)

{

int
sum = 

;

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

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

sum += j;

return
sum;

}

public
static
void
main(String[] args)

{

int
n = 
10
;

System.out.println(sumOfSeries(n));

}

}

## Python

def
sumOfSeries(n):

return
sum
([i
*
(i
+
1
)
/
2
for
i 
in
range
(
1
, n 
+
1
)])

if
__name__ 
=
=
"__main__"
:

n 
=
10

print
(sumOfSeries(n))

## C#

using
System;

class
GFG {

static
int
sumOfSeries(
int
n)

{

int
sum = 0;

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

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

sum += j;

return
sum;

}

public
static
void
Main()

{

int
n = 10;

Console.Write(sumOfSeries(n));

}

}

## PHP

<?php

function
sumOfSeries(
$n ) { $sum
= 0;

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

for
(
$j = 1 ;  $j
<= 
$i ;  $j
++)

$sum +=  $j
;

return
$sum ; } $n
= 10;

echo
(sumOfSeries(
$n )); ?> ## Javascript <script> function sumOfSeries(n) { let sum = 0; for (let i = 1 ; i <= n ; i++) for (let j = 1 ; j <= i ; j++) sum += j; return sum; } let n = 10; document.write(sumOfSeries(n)); </script> Output : 220 Efficient Approach : Letterm of the series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4)…(1 + 2 + 3 +..n) be denoted as an  an = Σn 1 = = Sum of n-terms of series Σn 1 an = Σn 1 = Σ + Σ = * + * =  Below is implementation of above approach : Baca : Contoh Pemuaian Zat Padat Dalam Kehidupan Sehari Hari ## C++ #include <bits/stdc++.h> using namespace std; int sumOfSeries( int n) { return (n * (n + 1) * (2 * n + 4)) / 12; } int main() { int n = 10; cout << sumOfSeries(n); } ## Java import java.util.*; class GFG { static int sumOfSeries( int n) { return (n * (n +  1 ) * ( 2 * n +  4 )) /  12 ; } public static void main(String[] args) { int n =  10 ; System.out.println(sumOfSeries(n)); } } ## Python def sumOfSeries(n): return (n  * (n  + 1 )  * ( 2 * n  + 4 ))  / 12 ; if __name__  = = '__main__' : n  = 10 print (sumOfSeries(n)) ## C# using System; class GFG { static int sumOfSeries( int n) { return (n * (n + 1) * (2 * n + 4)) / 12; } public static void Main() { int n = 10; Console.Write(sumOfSeries(n)); } } ## PHP <?php function sumOfSeries( $n
)

{

return
(
$n * ( $n
+ 1) *

(2 * 
$n + 4)) / 12; } $n
= 10;

echo
(sumOfSeries(
\$n
));

?>

## Javascript

<script>

function
sumOfSeries(n)

{

return
(n * (n + 1) *

(2 * n + 4)) / 12;

}

let n = 10;

document.write(sumOfSeries(n));

</script>

Output :

220

Time Complexity:
O(1)
Auxiliary Space:
O(1)

### 1 2 1 3 1 4

Sumber: https://www.geeksforgeeks.org/sum-of-the-series-1-12-123-1234-1234-n/

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