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Find the value of ln(N!) using Recursion using C++.
Suppose we have a number N, our task is to find ln(N!) using recursion. ln() is basically log base e. To solve this we can use this formula −
$$\ln\lgroup N!\rgroup=\ln\lgroup N*\lgroup N-1\rgroup *\lgroup N-2\rgroup *\dotsm*2*1\rgroup=\ln\lgroup N\rgroup+\ln\lgroup N+1\rgroup+\dotsm+\ln\lgroup 1\rgroup$$
Example
#include<iostream> #include<cmath> using namespace std; double factLog(int n) { if (n <= 1) return 0; return factLog(n - 1) + log(n); } int main() { int N = 3; cout << factLog(N); }
Output
1.79176
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