# 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


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 terms for 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  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

 // javaProgram 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

 # Python 3 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

 

Output:

22


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