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Daftar Isi:
Sum of the series 1 + (1+2) + (1+2+3) + (1+2+3+4) + …… + (1+2+3+4+…+n)
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 :
Let
term 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
![]](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-3bd5d776ed7afadcef473636fc1fe45f_l3.png "Rendered by QuickLaTeX.com")
+ Σ
=
*
+
*
=
Below is implementation of above approach :
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/
