Dado un entero positivo n y la tarea es encontrar la suma de la serie 1 + 2 + 2 + 3 + 3 + 3 + . . . + n.
Ejemplos:
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
Método de adición: En el método de adición se suman todos los elementos uno por uno.
A continuación se muestra la implementación de este enfoque.
C++
// 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
// 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
# 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#
// 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
<?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.
?>
Javascript
<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>
Producción:
385
Complejidad temporal: O(n 2 )
Espacio auxiliar: O(1)
Método de multiplicación: En el método de multiplicación cada elemento se multiplica por sí mismo y luego se suma.
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
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)
{
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
// 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
# 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#
// 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
<?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.
?>
Javascript
<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>
Producción:
385
Complejidad de tiempo: O(n)
Espacio auxiliar: O(1)
Usando la fórmula: También usamos la fórmula para encontrar la suma de 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++
// 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
// 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
# 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#
// 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
// 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.
?>
Javascript
<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>
Producción :
385
Complejidad de tiempo: O(1)
Espacio auxiliar: O(1)
Consulte la suma de cuadrados de números naturales para obtener detalles de la fórmula anterior y más optimizaciones.
Publicación traducida automáticamente
Artículo escrito por Dharmendra_Kumar y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA