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The reason why the factorial of 0 is 1 In my opinion, it is inappropriate for some people to deduce 0! = 1 by using the factorial recurrence formula The premise of recurrence formula n! = n * (n-1)! Is n > 1, so it is wrong to substitute 1 to get 0! = 1 Factorial is defined as n! = 1 * 2 * 3 *. * n or n! = n *. * 3 * 2 * 1, starting from or ending at 1 So 1! = 1 * 1 and not equal to 1 * 0! =In the permutation formula, P = n! / (m-n)! In order to make the equation hold when m = n, the denominator cannot be 0, so 0! = 1 is specified. Moreover, we know that there is only one way to take n elements from n elements, so it can only be specified equal to 1, not equal to 2, 3 The last sentence is wrong. There are n! Ways to take n elements from n non primes, so p = n, so 0! = 1 cannot be equal to 2,3
0! Equal to 1 is defined to make it meaningful when combined with other operations
In some programming, there may be n!
You can only for I: = 1 to n do TMP: = TMP * I; (Pascal)
The initial value of TMP can only be 1, otherwise there will be a problem
RELATED INFORMATIONS
- 1. How many zeros are there at the end of the factorial of 100?
- 2. 24 points of 9 5 7 5 (factorial)
- 3. On factorial If (2n)! = 2x4x6x Why not just write (2n)!, these two are not the same? Or n!
- 4. The factorial of minus one? It's when I solve the problem, that means I'm wrong,
- 5. It is required to define a function named mysum with a return value of double type. Its function is to find the sum of the number of two double types A) mysum(double a,b) { return (a+b); } B) mysum(double a,double b) { return a+b; } C) double mysum(int a,intb); {return a+b; } D) double mysum(double a,double b) { retrun (a+b); } What is the correct answer and why? I see. I didn't see the title "finding the sum of two double type numbers". Now the question is what type is the return value of B? Do you have to write the brackets of return (a + b)? C linguistics is not good, there are many fuzzy places
- 6. A defined function has a return value. Function calls can be used as formal parameters of a function? If a defined function has a return value, the error in the following description of the function call is d A) Function calls can exist as separate statements B) Function calls can be used as arguments to a function C) Function calls can appear in expressions D) Function calls can be used as formal parameters of a function Many of the answers come from D!
- 7. Define the function Total (n), calculate 1 + 2 + 3 +... + N, the function return type is int In the main function input positive integer n, call the function Total (n) to calculate and output the value of the following formula S=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n) My answer is: #include int total(int x) { int z=0; for(;x>0;x--) z=z+x; return z; } void main() { int n; double a; a=0; Printf ("please enter a positive integer n / N"); scanf("%d",&n); for(;n>0;n--) a=a+1/total(n); printf("%lf\n",a); } Then the output result should be the wrong data type
- 8. If a single variable polynomial is represented by a circularly linked list, try to write a function Calc (x) to calculate the value of the polynomial at X #include //#include using namespace std; class polynomial { public: float coef; int exp; polynomial *next; //void count(polynomial *p,int x); }; int main() { void count(polynomial *p,int x); // string str; polynomial *p; p=new polynomial; int e; float c; polynomial *q,*r; q=p; r=p; // coutexp=e; r->next=q; r=q; } // cout>x; count(p,x); return 0; } void count(polynomial *p,int x) { float c; int e; int f=1; float num=0; polynomial *k,*m; k=p; m=p; while(k!=m) { c=k->coef; e=k->exp; p=k->next; k=p; if(e>=1) { for(e;e>0;e--) { f=x*f; num+=c*f; } f=1; } if(e==0) num+=c; if(e
- 9. double fact(int n) { if (n==0) return 1; else return n*(fact(n-1)); }
- 10. Why do mathematicians stipulate that the factorial of 0 is 1?
- 11. Why is 0 factorial 1,1 factorial 1,2 factorial 2?
- 12. How many zeros are there at the end of the factorial of 25?
- 13. How many consecutive zeros are there at the end of the factorial in 2013?
- 14. How many zeros are there at the end of the factorial of 35? 35*34*33…… *3 * 2 * 1 the answer is 8,
- 15. How many zeros are there at the end of the factorial of 100
- 16. If a, B and C are three digits of a three digit number, and a ≤ B ≤ C, what is the maximum value of | A-B | + | B-C | + | C-A |?
- 17. If A.B.C is a three digit number of hundred, ten and one, and a ≤ B ≤ C, then the maximum value of | A-B | + | B-C | + | C-A |,
- 18. Let a, B and C be a three digit number of hundred, ten and one respectively, and a ≤ B ≤ C, then the maximum value that | A-B | + | B-C | + | C-A | can obtain is______ ．
- 19. a. B, C are three digit hundreds, tens and ones, and a Who can help me? My wealth is zero
- 20. For a three digit number, a hundred digit number is a, a ten digit number is B, and a single digit number is C, and a > C, exchange the position of a hundred digit number and a single digit number to get a new three digit number, please explain: The difference between the original three digits and the new three digits must be a multiple of 99