Question

 How to find the value y from  this polynomial y = (x-1/x)+(x-1/x)²/2+(x-1/x)³/3+(x-1/x)⁴/4

Answer 1

Either using loop or Recursive function , the result can be achieved . 

import java.util.Scanner;

public class Main

{

  public static void main (String[]args)

  {

    try

    {

      Scanner scanner = new Scanner (System.in);

      System.out.print ("Enter X Value : ");

      int x = scanner.nextInt ();

      int limit = 4;

      double y = 0;

      for (int i = 1; i <= limit; i++)

                    y += returnMultiply (x, i);

      System.out.println ("Y : " + y);

    }

    catch (Exception ex)

    {

      ex.printStackTrace ();

    }

  }

  private static double returnMultiply (int x, int power)

  {

    double result = 1;

    for (int i = 1; i <= power; i++)

           result *= (double) (x - 1) / x;

    return (double) result / power;

  }

}

Answer 2

In Python using recursion:

def recur(x, steps = 4):
    if steps > 0:
        return (x**steps) + recur(x, steps - 1)
    else:
        return 0

x = 2
x_n = (x-1)/x
print(recur(x_n, 4))

 and iteration:

x = 2, steps = 4
y, x_n = 0, (x-1)/x
for s in range(1, steps + 1):
    y += (x_n**s)/s

print(y)

Answer 3

clc                                                                                                           @matlab

syms x y

a=input('enter the polynomial');                                                            

b=simplify(a);

disp(b);

output

enter the polynomial

(x-1)/x+((x-1)/x)^2/2+((x-1)/x)^3/3+((x-1)/x)^4/4

(25*x^4 - 48*x^3 + 36*x^2 - 16*x + 3)/(12*x^4)

Answer 4

#include<stdio.h>

#include<math.h>

# define term 4//term of series can be change from here

int main()

{

float a,i,sum=0,x;

printf("enter the value of x :");

scanf("%f",&x);

a=(x-1/x);

for(i=1;i<=term;i++)

{

sum+=pow(a,i)/i;

}printf("sum of series is %f",sum);

return 0;

}