# Sum of series M/1 + (M+P)/2 + (M+2*P)/4 + (M+3*P)/8……up to infinite

Find the sum of series M/1 + (M+P)/2 + (M+2*P)/4 + (M+3*P)/8……up to infinite where M and P are positive integers.

Examples:

Input : M = 0, P = 3; Output : 6 Input : M = 2, P = 9; Output : 22

**Method : ****S = M/1 + (M + P)/2 + (M + 2*P)/4 + (M + 3*P) / 8……up to infinite**

so the solution of this series will be like this

we are going to divide this series into two parts-

S = (M/1 + M/2 + M/4 + M/8……up to infinite) + ( p/2 + (2*p)/4 + (3*p)/8 + ….up to infinite)

let us consider it**S = A + B ……..eq(1)**

where,

A = M/1 + M/2 + M/4 + M/8……up to infinite

A = M*(1 + 1/2 + 1/4 + 1/8….up to infinite)

which is G.P of infinite terms with r = 1/2;

According to the formula of G.P sum of infinite termsfor r < 1 and

a is first term and r is common ratio so now,

A = M * ( 1 / (1 – 1/2) )

A = 2 * M ;

**Now for B –**

B = ( p/2 + (2*p)/4 + (3*p)/8 + ….up to infinite)

B = P/2 * ( 1 + 2*(1/2) + 3*(1/4) + ……up to infinite)

it is sum of AGP of infinite terms with a = 1, r = 1/2 and d = 1;

According to the formula where a is first term,

r is common ratio and d is common difference so now,

B = P/2 * ( 1 / (1-1/2) + (1*1/2) / (1-1/2)^2 )

B = P/2 * 4

B = 2*P ;

put value of A and B in eq(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

`// 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)) ;` ` ` `}` `}` |

## Python3

`# 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)) ;` ` ` `}` `}` |

## PHP

`<?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` `?>` |

## Javascript

`<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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