数列 M/1+(M+P)/2+(M+2 * P)/4+(M+3 * P)/8 的和……直到无穷大
原文:https://www . geesforgeks . org/find-sum-series-m-1-MP2-m2p 4-m3p 8-infinite/
求数列 M/1+(M+P)/2+(M+2 * P)/4+(M+3 * P)/8……直到无穷的和，其中 M 和 P 是正整数。
示例:
Input : M = 0, P = 3;
Output : 6
Input : M = 2, P = 9;
Output : 22
方法:
S = M/1+(M+P)/2+(M+2 * P)/4+(M+3 * P)/8……直到无穷
所以这个系列的解会是这样的
我们要把这个系列分成两部分-
S =(M/1+M/2+M/4+M/8……直到无穷)+ ( p/2 + (2p)/4 + (3p)/8 + …。高达无限)
我们来考虑一下
S = A + B ……..等式(1)
其中，
A = M/1+M/2+M/4+M/8……直到无穷大
A = M (1+1/2+1/4+1/8……。直到无限)
是 r = 1/2 的无限项的 G . P；
根据无限项的 G.P 和公式
为 r < 1 而
a 为第一项，r 为公比所以现在，
A = M (1/(1–1/2))
A = 2 * M；
现在为 B–
B =(p/2+(2 * p)/4+(3 * p)/8+…。直到无限)
B = P/2 (1+2 (1/2)+3 (1/4)+……直到无限)
它是 a = 1，r = 1/2，d = 1 的无限项 AGP 之和；
根据公式
其中 a 为第一项，
r 为公比，d 为公差所以现在，
b = p/2 (1/(1-1/2)+(1 * 1/2)/(1-1/2)^2)
b = p/2 * 4
b = 2 * p；
将 A 和 B 的值放入等式(1)
S = 2(M + P)
C++
#include <iostream>
using namespace std;
int sum(int M, int P)
{
return 2*(M + P);
}
// driver code
int main() {
int M = 2, P = 9;
cout << sum(M,P);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to finding the
// sum of the series
import java.io.*;
class GFG {
// function that calculate
// the sum of the nth series
static int sum_series(int M, int P)
{
return 2 * (M + P);
}
// Driver function
public static void main (String[] args)
{
int M = 2;
int P = 9;
System.out.println( sum_series(M, P)) ;
}
}
Python 3
# Python3 Program to finding
# the sum of the series
# function that calculate
# the sum of the series
def sum_series(M, P):
return int(2 * (M + P))
# Driver function
M = 2
P = 9
print(sum_series(M ,P))
C
// C# program to finding the
// sum of the series
using System;
class GFG {
// Function that calculate
// the sum of the nth series
static int sum_series(int M, int P)
{
return 2*(M + P);
}
// Driver Code
public static void Main ()
{
int M =2;
int P =9;
Console.Write( sum_series(M,P)) ;
}
}
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to finding the
// sum of the series
// Function that calculate
// the sum of the nth series
function sum($M, $P)
{
return 2*($M + $P);
}
// Driver Code
$M = 2;
$P = 9;
echo sum($M, $P);
// This code is contributed by mits
?>
java 描述语言
<script>
// JavaScript program to finding the
// sum of the series
// Function that calculate
// the sum of the nth series
function sum_series(M, P)
{
return 2 * (M + P);
}
// Driver code
let M = 2;
let P = 9;
document.write( sum_series(M, P));
// This code is contributed by splevel62
</script>
Output:
22
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