Given a value n, the task is to find sum of the series (1*2) + (2*3) + (3*4) + ……+ n terms
Examples:
Input: n = 2
Output: 8
Explanation:
(1*2) + (2*3)
= 2 + 6
= 8
Input: n = 3
Output: 20
Explanation:
(1*2) + (2*3) + (2*4)
= 2 + 6 + 12
= 20
Simple Solution One by one add elements recursively.
Below is the implementation
C++
#include <bits/stdc++.h>
using namespace std;
int sum( int n)
{
if (n == 1) {
return 2;
}
else {
return (n * (n + 1) + sum(n - 1));
}
}
int main()
{
int n = 2;
cout << sum(n);
}
|
Java
class Solution {
static int sum( int n)
{
if (n == 1 ) {
return 2 ;
}
else {
return (n * (n + 1 ) + sum(n - 1 ));
}
}
public static void main(String args[])
{
int n = 2 ;
System.out.println(sum(n));
}
}
|
Python3
def sum (n):
if (n = = 1 ):
return 2 ;
else :
return (n * (n + 1 ) + sum (n - 1 ));
n = 2 ;
print ( sum (n));
|
C#
using System;
class Solution {
static int sum( int n)
{
if (n == 1) {
return 2;
}
else {
return (n * (n + 1) + sum(n - 1));
}
}
public static void Main()
{
int n = 2;
Console.WrieLine(sum(n));
}
}
|
PHP
<?php
function sum( $n )
{
if ( $n == 1)
{
return 2;
}
else
{
return ( $n * ( $n + 1) +
sum( $n - 1));
}
}
$n = 2;
echo sum( $n );
?>
|
Javascript
<script>
function sum(n)
{
if (n == 1) {
return 2;
}
else {
return (n * (n + 1) + sum(n - 1));
}
}
n = 2;
document.write(sum(n));
</script>
|
Auxiliary Space: O(n), since n extra space has been taken.
Efficient Solution We can solve this problem using direct formula.
Sum can be written as below
?(n * (n+1))
?(n*n + n)
= ?(n*n) + ?(n)
We can apply the formulas for sum squares of natural number and sum of natural numbers.
= n(n+1)(2n+1)/6 + n*(n+1)/2
= n * (n + 1) * (n + 2) / 3
C++
#include <bits/stdc++.h>
using namespace std;
int sum( int n)
{
return n * (n + 1) * (n + 2) / 3;
}
int main()
{
int n = 2;
cout << sum(n);
}
|
Java
class GFG
{
static int sum( int n)
{
return n * (n + 1 ) * (n + 2 ) / 3 ;
}
public static void main(String[] args)
{
int n = 2 ;
System.out.println(sum(n));
}
}
|
Python3
def Sum (n):
return n * (n + 1 ) * (n + 2 ) / / 3
if __name__ = = "__main__" :
n = 2 ;
print ( Sum (n))
|
C#
using System;
class GFG
{
static int sum( int n)
{
return n * (n + 1) * (n + 2) / 3;
}
public static void Main(String[] args)
{
int n = 2;
Console.WriteLine(sum(n));
}
}
|
PHP
<?php
function sum( $n )
{
return $n * ( $n + 1) * ( $n + 2) / 3;
}
$n = 2;
echo sum( $n );
?>
|
Javascript
<script>
function sum(n)
{
return n * (n + 1) * (n + 2) / 3;
}
var n = 2;
document.write(sum(n));
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
Contact Us