求数列 1、2、3、6、9、18、27、54、…的和，直到 N 项
原文:https://www . geesforgeks . org/find-the-sum-the-series-1-2-3-6-9-18-27-54-till-n-terms/
给定一个数字 N ，任务是找到下面系列的和，直到 N 项。
例:
输入: N = 8 输出:201 1+2+3+6+9+18+27+54+81 = 201 输入: N = 12 输出:1821 1+2+3+6+9+18+27+54+81+162+243+486+729 = 0
方法:从给定的序列中，找到第 n 项的公式:
1st term = 1
2nd term = 2 = 2 * 1
3rd term = 3 = 3/2 * 2
4th term = 6 = 2 * 3
5th term = 9 = 3/2 * 6
6th term = 18 = 2 * 9
.
.
Nth term = [2 * (N-1)th term], if N is even
[3/2 * (N-1)th term], if N is odd
因此:
该系列的第 n 项
``` *** QuickLaTeX cannot compile formula:
*** Error message: Error: Nothing to show, formula is empty
```
然后在【1，N】范围内的数字上迭代，使用上面的公式找到所有的项，并计算它们的和。 方法:通过观察给定序列中的模式，序列的下一个数字交替乘以 2 和 3/2 。 以下是上述方法的实施:
C++
// C++ program for the above series
#include <iostream>
using namespace std;
// Function to find the sum of series
void printSeriesSum(int N)
{
double sum = 0;
int a = 1;
int cnt = 0;
// Flag to find the multiplicating
// factor.. i.e, by 2 or 3/2
bool flag = true;
// First term
sum += a;
while (cnt < N) {
int nextElement;
// If flag is true, multiply by 2
if (flag) {
nextElement = a * 2;
sum += nextElement;
flag = !flag;
}
// If flag is false, multiply by 3/2
else {
nextElement = a * 3 / 2;
sum += nextElement;
flag = !flag;
}
// Update the previous element
// to nextElement
a = nextElement;
cnt++;
}
// Print the sum
cout << sum << endl;
}
// Driver Code
int main()
{
int N = 8;
printSeriesSum(N);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program for the above series
class GFG {
// Function to find the sum of series
static void printSeriesSum(int N)
{
double sum = 0;
int a = 1;
int cnt = 0;
// Flag to find the multiplicating
// factor.. i.e, by 2 or 3/2
boolean flag = true;
// First term
sum += a;
while (cnt < N) {
int nextElement;
// If flag is true, multiply by 2
if (flag == true) {
nextElement = a * 2;
sum += nextElement;
flag = !flag;
}
// If flag is false, multiply by 3/2
else {
nextElement = a * 3 / 2;
sum += nextElement;
flag = !flag;
}
// Update the previous element
// to nextElement
a = nextElement;
cnt++;
}
// Print the sum
System.out.println(sum);
}
// Driver Code
public static void main (String[] args)
{
int N = 8;
printSeriesSum(N);
}
}
// This code is contributed by AnkitRai01
Python 3
# Python3 program for the above series
# Function to find the sum of series
def printSeriesSum(N) :
sum = 0;
a = 1;
cnt = 0;
# Flag to find the multiplicating
# factor.. i.e, by 2 or 3/2
flag = True;
# First term
sum += a;
while (cnt < N) :
nextElement = None;
# If flag is true, multiply by 2
if (flag) :
nextElement = a * 2;
sum += nextElement;
flag = not flag;
# If flag is false, multiply by 3/2
else :
nextElement = a * (3 / 2);
sum += nextElement;
flag = not flag;
# Update the previous element
# to nextElement
a = nextElement;
cnt += 1
# Print the sum
print(sum);
# Driver Code
if __name__ == "__main__" :
N = 8;
printSeriesSum(N);
# This code is contributed by AnkitRai01
C
// C# program for the above series
using System;
class GFG {
// Function to find the sum of series
static void printSeriesSum(int N)
{
double sum = 0;
int a = 1;
int cnt = 0;
// Flag to find the multiplicating
// factor.. i.e, by 2 or 3/2
bool flag = true;
// First term
sum += a;
while (cnt < N) {
int nextElement;
// If flag is true, multiply by 2
if (flag == true) {
nextElement = a * 2;
sum += nextElement;
flag = !flag;
}
// If flag is false, multiply by 3/2
else {
nextElement = a * 3 / 2;
sum += nextElement;
flag = !flag;
}
// Update the previous element
// to nextElement
a = nextElement;
cnt++;
}
// Print the sum
Console.WriteLine(sum);
}
// Driver Code
public static void Main (string[] args)
{
int N = 8;
printSeriesSum(N);
}
}
// This code is contributed by AnkitRai01
java 描述语言
<script>
// javascript program for the above series
// Function to find the sum of series
function printSeriesSum( N)
{
let sum = 0;
let a = 1;
let cnt = 0;
// Flag to find the multiplicating
// factor.. i.e, by 2 or 3/2
let flag = true;
// First term
sum += a;
while (cnt < N) {
let nextElement;
// If flag is true, multiply by 2
if (flag) {
nextElement = a * 2;
sum += nextElement;
flag = !flag;
}
// If flag is false, multiply by 3/2
else {
nextElement = a * 3 / 2;
sum += nextElement;
flag = !flag;
}
// Update the previous element
// to nextElement
a = nextElement;
cnt++;
}
// Print the sum
document.write(sum );
}
// Driver Code
let N = 8;
printSeriesSum(N);
// This code is contributed by todaysgaurav
</script>
Output:
201
时间复杂度:0(N)
辅助空间:0(1)
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