Dado un número n, encuentra el término n-ésimo en la serie 1, 3, 6, 10, 15, 21…
Ejemplos:
Input : 3 Output : 6 Input : 4 Output : 10
Las series dadas representan números triangulares que son sumas de números naturales.
Enfoque ingenuo:
la serie representa básicamente sumas de números naturales. El primer término es la suma de un solo número. El segundo término es la suma de dos números, y así sucesivamente. Una solución simple es sumar los primeros n números naturales.
C++
// CPP program to find n-th term of
// series 1, 3, 6, 10, 15, 21...
#include <iostream>
using namespace std;
// Function to find the nth term of series
int term(int n)
{
// Loop to add numbers
int ans = 0;
for (int i = 1; i <= n; i++)
ans += i;
return ans;
}
// Driver code
int main()
{
int n = 4;
cout << term(n) ;
return 0;
}
Java
// Java program to find n-th term of
// series 1, 3, 6, 10, 15, 21...
import java.io.*;
class GFG {
// Function to find the nth term of series
static int term(int n)
{
// Loop to add numbers
int ans = 0;
for (int i = 1; i <= n; i++)
ans += i;
return ans;
}
// Driver code
public static void main(String args[])
{
int n = 4;
System.out.println(term(n));
}
}
// This code is contributed by Nikita Tiwari.
Python3
# Python 3 program to find # n-th term of # series 1, 3, 6, 10, 15, 21... # Function to find the # nth term of series def term(n) : # Loop to add numbers ans = 0 for i in range(1,n+1) : ans = ans + i return ans # Driver code n = 4 print(term(n)) # This code is contributed # by Nikita Tiwari.
C#
// C# program to find n-th term of
// series 1, 3, 6, 10, 15, 21...
using System;
class GFG {
// Function to find the nth term
// of series
static int term(int n)
{
// Loop to add numbers
int ans = 0;
for (int i = 1; i <= n; i++)
ans += i;
return ans;
}
// Driver code
public static void Main()
{
int n = 4;
Console.WriteLine(term(n));
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP program to find n-th term of
// series 1, 3, 6, 10, 15, 21...
// Function to find the nth
// term of series
function term($n)
{
// Loop to add numbers
$ans = 0;
for ($i = 1; $i <= $n; $i++)
$ans += $i;
return $ans;
}
// Driver code
$n = 4;
echo(term($n)) ;
// This code is contributed by Ajit.
?>
Javascript
<script>
// Javascript program to find n-th term of
// series 1, 3, 6, 10, 15, 21...
// Function to find the nth term of series
function term(n)
{
// Loop to add numbers
let ans = 0;
for(let i = 1; i <= n; i++)
ans += i;
return ans;
}
// Driver code
let n = 4;
document.write(term(n));
// This code is contributed by rishavmahato348
</script>
Producción:
10
Complejidad de tiempo : O (N), ya que estamos usando un bucle para atravesar N veces.
Espacio auxiliar : O(1), ya que no estamos utilizando ningún espacio adicional.
Enfoque eficiente:
El patrón en esta serie es que el término n es igual a la suma de (n-1) el término y n .
Ejemplo :
n = 2 2nd term equals to sum of 1st term and 2 i.e A2 = A1 + 2 = 1 + 2 = 3 Similarly, A3 = A2 + 3 = 3 + 3 = 6 and so on..
Obtenemos:
A(n) = A(n - 1) + n
= A(n - 2) + n + (n - 1)
= A(n - 3) + n + (n - 1) + (n - 2)
.
.
.
= A(1) + 2 + 3... + (n-1) + n
A(n) = 1 + 2 + 3 + 4... + (n - 1) + n
= n(n + 1) / 2
i.e A(n) is sum of First n natural numbers.
A continuación se muestra la implementación del enfoque anterior:
C++
// CPP program to find the n-th
// term in series 1 3 6 10 ...
#include <bits/stdc++.h>
using namespace std;
// Function to find nth term
int term(int n)
{
return n * (n + 1) / 2;
}
// Driver code
int main()
{
int n = 4;
cout << term(n);
return 0;
}
Java
// Java program to find the n-th
// term in series 1 3 6 10 ...
import java.io.*;
class Series {
// Function to find nth term
static int term(int n){
return n * (n + 1) / 2;
}
// Driver Code
public static void main (String[] args) {
int n = 4;
System.out.println(term(n));
}
}
// This code is contributed by Chinmoy Lenka
Python
# Python program to find the Nth # term in series 1 3 6 10 ... # Function to print nth term # of series 1 3 6 10 .... def term(n): return n *(n + 1) / 2 # Driver code n = 4 print term(n)
C#
// C# program to find the n-th
// term in series 1 3 6 10 ...
using System;
class GFG {
// Function to find nth term
static int term(int n)
{
return n * (n + 1) / 2;
}
// Driver Code
public static void Main()
{
int n = 4;
Console.WriteLine(term(n));
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP program to find the n-th
// term in series 1 3 6 10 ...
// Function to find nth term
function term($n)
{
return $n * ($n + 1) / 2;
}
// Driver code
$n = 4;
echo(term($n));
// This code is contributed by Ajit.
?>
Javascript
<script>
// Javascript program to find the n-th
// term in series 1 3 6 10 ...
// Function to find nth term
function term(n)
{
return parseInt(n * (n + 1) / 2);
}
// Driver code
let n = 4;
document.write(term(n));
// This code is contributed by subhammahato348.
</script>
Producción :
10
Complejidad de tiempo : O (1), ya que no estamos usando ningún bucle o recursión para atravesar.
Espacio auxiliar : O(1), ya que no estamos utilizando ningún espacio adicional.