有限幾何級数2

y[n] = x⁰ + x¹ + x² + x³ + ...... + xⁿ-1は、|x|<1のときy[∞] = 1/(1 - x)である。
x=0.5のときnが最低いくつであればn=∞のときの真値2.0との誤差が0.1%未満になるか。
finiteGeom_2.vi - Google ドライブ

.tns

ceiling(right(solve(abs(1-((∑(x^(n-1),n,1,n_min))/(((−1)/(x-1)))))*100<percent,n_min)))|x=((1)/(2)) and percent=((1)/(10))

.py

x          = 0.5
trueVal    = 1/(1 - x)
maxPercent = 0.1
    
total = 0
for n in range(1, 999):
    total += x**(n-1)
    deviationPercent = abs(1 - (total/trueVal)) * 100
    print("n: %2d, total: %0.6f, trueVal: %.1f, deviationPercent: %6.3f%%" % (n, total, trueVal, deviationPercent))
    if deviationPercent < maxPercent:
        break

.cpp

#include <iostream>
#include <cmath>
using namespace std;

int main(){
    double x          = 0.5;
    double trueVal    = 1.0/(1.0 - x);
    double maxPercent = 0.1;

    double total      = 0.0;
    for(int n=1; n<999; n++){
        total += pow(x, (n-1));
        double deviationPercent = abs(1.0 - (total/trueVal)) * 100.0;
        printf("n: %2d, total: %.6f, trueVal: %.2f, deviationPercent: %6.3f%%\n", n, total, trueVal, deviationPercent);
        if(deviationPercent < maxPercent){
            break;
        }
    }


    return 0;
}