Recursively find the partial sum of simple alternating power series (15 points)

6-12【 Extended programming problems _ Practice after class 】【 Chen Yue textbook exercises 2.6】 Recursively find the partial sum of simple alternating power series (15 branch )

This question requests to realize a function , Calculate the partial sum of the following simple alternating power series ：

​
Function interface definition ：
double fn( double x, int n );

The title guarantees the incoming n It's a positive integer. , And the input and output are in the double precision range . function fn The partial sum of the above series should be returned . It is recommended to try to implement .

Sample referee test procedure ：

#include <stdio.h>

double fn( double x, int n );

int main()
{
    
    double x;
    int n;

    scanf("%lf %d", &x, &n);
    printf("%.2f\n", fn(x,n));

    return 0;
}

/*  Your code will be embedded here  */

sample input ：

0.5 12

sample output ：

0.33

This problem tries to find rules by mathematical induction in order to use recursion ,
Then, inexplicably, we get the following formula .... Cry
Code ：

double fn(double x, int n)
{
    
    if (n == 1)return x;
    else{
    
        return -fn(x,n - 1) * x + x;
    }
}