给定正整数n 。问题是找到给定序列1 +(1 + 2)+(1 + 2 + 3)+(1 + 2 + 3 + 4)+……+(1 + 2 + 3 + 4 +…的总和。 + n) ,其中系列中的第i个项是第一个i个奇数自然数的总和。
例子:
Input : n = 2
Output : 5
(1) + (1+3) = 5
Input : n = 5
Output : 55
(1) + (1+3) + (1+3+5) + (1+3+5+7) + (1+3+5+7+9) = 55
天真的方法:使用两个循环获得每个第i个项的总和,然后将这些总和加到最终总和上。
C++
// C++ implementation to find the
// sum of the given series
#include
using namespace std;
// functionn to find the
// sum of the given series
int sumOfTheSeries(int n)
{
int sum = 0;
for (int i = 1; i <= n; i++) {
// first term of each i-th term
int k = 1;
for (int j = 1; j <= i; j++) {
sum += k;
// next term
k += 2;
}
}
// required sum
return sum;
}
// Driver program
int main()
{
int n = 5;
cout << "Sum = "
<< sumOfTheSeries(n);
return 0;
}
Java
// Java implementation to find
// the sum of the given series
import java.util.*;
class GFG {
// functionn to find the sum
// of the given series
static int sumOfTheSeries(int n)
{
int sum = 0;
for (int i = 1; i <= n; i++)
{
// first term of each
// i-th term
int k = 1;
for (int j = 1; j <= i; j++)
{
sum += k;
// next term
k += 2;
}
}
// required sum
return sum;
}
/* Driver program */
public static void main(String[] args)
{
int n = 5;
System.out.println("Sum = " +
sumOfTheSeries(n));
}
}
// This code is contributed by Arnav Kr. Mandal.
Python3
# Python3 implementation to find
# the sum of the given series
# functionn to find the sum
# of the given series
def sumOfTheSeries( n ):
sum = 0
for i in range(1, n + 1):
# first term of each i-th term
k = 1
for j in range(1,i+1):
sum += k
# next term
k += 2
# required sum
return sum
# Driver program
n = 5
print("Sum =", sumOfTheSeries(n))
# This code is contributed by "Sharad_Bhardwaj".
C#
// C# implementation to find
// the sum of the given series
using System;
class GFG {
// functionn to find the sum
// of the given series
static int sumOfTheSeries(int n)
{
int sum = 0;
for (int i = 1; i <= n; i++) {
// first term of each
// i-th term
int k = 1;
for (int j = 1; j <= i; j++) {
sum += k;
// next term
k += 2;
}
}
// required sum
return sum;
}
/* Driver program */
public static void Main()
{
int n = 5;
Console.Write("Sum = " +
sumOfTheSeries(n));
}
}
// This code is contributed by vt_m.
php
Javascript
C++
// C++ implementation to find the sum
// of the given series
#include
using namespace std;
// functionn to find the sum
// of the given series
int sumOfTheSeries(int n)
{
// required sum
return (n * (n + 1) / 2) *
(2 * n + 1) / 3;
}
// Driver program to test above
int main()
{
int n = 5;
cout << "Sum = "
<< sumOfTheSeries(n);
return 0;
}
Java
// Java implementation to find
// the sum of the given series
import java.io.*;
class GfG {
// function to find the sum
// of the given series
static int sumOfTheSeries(int n)
{
// required sum
return (n * (n + 1) / 2) *
(2 * n + 1) / 3;
}
// Driver program to test above
public static void main (String[] args)
{
int n = 5;
System.out.println("Sum = "+
sumOfTheSeries(n));
}
}
// This code is contributed by Gitanjali.
Python3
# Python3 implementation to find
# the sum of the given series
# functionn to find the sum
# of the given series
def sumOfTheSeries( n ):
# required sum
return int((n * (n + 1) / 2) *
(2 * n + 1) / 3)
# Driver program to test above
n = 5
print("Sum =", sumOfTheSeries(n))
# This code is contributed by "Sharad_Bhardwaj".
C#
// C# implementation to find
// the sum of the given series
using System;
class GfG {
// function to find the sum
// of the given series
static int sumOfTheSeries(int n)
{
// required sum
return (n * (n + 1) / 2) *
(2 * n + 1) / 3;
}
// Driver program to test above
public static void Main()
{
int n = 5;
Console.Write("Sum = " +
sumOfTheSeries(n));
}
}
// This code is contributed by vt_m.
PHP
Javascript
输出:
Sum = 55
高效方法:
令n为给定级数的第n个项。
an = (1 + 3 + 5 + 7 + (2n-1))
= sum of first n odd numbers
= n2
有关以上公式的证明,请参阅此帖子。
现在,
有关以上公式的证明,请参阅此帖子。
C++
// C++ implementation to find the sum
// of the given series
#include
using namespace std;
// functionn to find the sum
// of the given series
int sumOfTheSeries(int n)
{
// required sum
return (n * (n + 1) / 2) *
(2 * n + 1) / 3;
}
// Driver program to test above
int main()
{
int n = 5;
cout << "Sum = "
<< sumOfTheSeries(n);
return 0;
}
Java
// Java implementation to find
// the sum of the given series
import java.io.*;
class GfG {
// function to find the sum
// of the given series
static int sumOfTheSeries(int n)
{
// required sum
return (n * (n + 1) / 2) *
(2 * n + 1) / 3;
}
// Driver program to test above
public static void main (String[] args)
{
int n = 5;
System.out.println("Sum = "+
sumOfTheSeries(n));
}
}
// This code is contributed by Gitanjali.
Python3
# Python3 implementation to find
# the sum of the given series
# functionn to find the sum
# of the given series
def sumOfTheSeries( n ):
# required sum
return int((n * (n + 1) / 2) *
(2 * n + 1) / 3)
# Driver program to test above
n = 5
print("Sum =", sumOfTheSeries(n))
# This code is contributed by "Sharad_Bhardwaj".
C#
// C# implementation to find
// the sum of the given series
using System;
class GfG {
// function to find the sum
// of the given series
static int sumOfTheSeries(int n)
{
// required sum
return (n * (n + 1) / 2) *
(2 * n + 1) / 3;
}
// Driver program to test above
public static void Main()
{
int n = 5;
Console.Write("Sum = " +
sumOfTheSeries(n));
}
}
// This code is contributed by vt_m.
的PHP
Java脚本
输出:
Sum = 55