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The meaning of mathematical symbols After opening the cube by 16 * 30 * 30 * 30 / 2, the number to be calculated is 8 * 30 * 30 * 30, and after opening the cube, it is 2 * 30 = 60cm Does the / in it mean division? There are also two such symbols ^ *Is this a multiplier sign?
/For division
^The number n, N, n is the power of n
*For multiplier
Specific meaning of all mathematical symbols
Quantity symbol
For example: I, 2 + I, a, x, natural logarithm base e, PI
Operation symbol
Such as plus sign (+), minus sign (-), multiplication sign (× or ·), division sign (△ or /), Union (∪), intersection (∩), root sign (√), logarithm (log, LG, LN), ratio (:), absolute value sign "|", differential (DX), integral (∫), curve integral (∮), etc
Relation symbol
If "=" is an equal sign, "≈" is an approximate sign, "≠" is an unequal sign and ">" is a greater than sign, "The implication relation between proposition a and B a * the dual formula wff of formula A and IFF if and only if ↑ the" and not "operation of the proposition (" and or not gate "), the" or not "operation (" or not gate ") of the proposition √ the modal word" necessity "} the modal word" possible "φ empty set ∈ belongs to a ∈ B Then the difference operation 〡 restriction of the difference operation 〡 of the power set ∉ a | set a belonging to B (∉ does not belong to) P (a) set a ∉ the number of points of a | a | set a R ^ 2 = R ⊆ R [R ^ n = R ^ (n-1) ⊆ R] relation R ⊂ alev ⊆ contains ⊂ (or add ≠ below) the difference operation 〡 set 〡 The cyclic group I (I capital) ring generated by the element a of the quotient set [a] of R with respect to r on the equivalence class a of [x] (lower right corner R) set with respect to relation R, Ideal Z / (n) module n congruence set R (R) relation R reflexive closure s (R) relation CP propositional Deduction Theorem (CP rule) eg existence extension rule (existence quantifier introduction rule) es existence quantifier specific rule (existence quantifier elimination rule) UG full name extension rule (full name quantifier introduction rule) us Full name specific rule (elimination rule of full name quantifier) r relation R compatible relation R o s relation and the compound domain of domf function (front field) range of ranf function f: X → Y F is the function from X to y GCD (x, y) x, y the greatest common divisor LCM (x, y) X, The distance between D (U, V) points u and V of the integer set D (U, V) points u and V of the set of integers D (U, V) points u and V with respect to the kernel (or F homomorphic kernel) of the left (right) coset Ker (f) homomorphic mapping f of a with the degree g = (V, e) point set v, Graph w (g) connected branches of graph G with edge set E K (g) vertex connectivity of graph G △ (g) maximum vertex degree a (g) adjacency matrix P (g) reachable matrix M (g) incidence matrix C complex set n natural number set (including 0) n * positive natural number set P prime set Q rational number set R real number set Z integer set set category top topological space category AB Abelian group category GRP group category mon element semigroup category ring ring (associative) ring category with identity element RNG ring category crng commutative ring category r-mod ring R left module category mod-r ring R right module category field domain category poset poset category
Symbol meaning = is equal to ≠ not equal to is not equal to < less than is less than > greater than than | parallel is parallel to ≥ is greater than or equal to ≤ less than or equal to ≡ equal to or congruent π PI | x| Absolute value of X
Is similar to ≌ congruence is equal to (specially for triangle) > > far greater than sign
Write a program to find 1! + 2! + N! Is required to input the value of N from the main function, use the function to realize the calculation of factorial, and return through the function value C language,
main()
{
int sum=0;
scanf("%d",n)
for(int i=n;i>0;i--)
{
int k=1;
for(int j=i;j>0;j--)
{
k=k*j;
}
sum+=k;
}
printf("%d",sum)
}
Input 3 integers x, y, Z to calculate and output s = x! + Y! + Z!. it is required to define two functions, one recursive function for factorial, and the other function for cumulative sum?
int function1(int x,int y,int z)
{
return function2(x)+ function2(y)+ function2(z);
}
int function2(int a)
{
int intResult;
for(int i=a;i
2. Test question (1) define the function fact (n) to calculate the factorial of N: = 1 * 2 * *n. The return value type of the function is double
double fact(int n){
double temp;
if(n==0||n==1)
return 1.0;
if(n>=2)
{
temp=double(n*fact(n-1));
rentun temp;
}
}
Enter a positive integer n, and find 1 + 1 / 2! + 1 / 3! + 1 / N! Is required to define and call the function fact (n) to calculate n kan shang mian
int jie_ cheng(int n)
{
if(n==1) return 1;
return n*jie_ cheng(n-1);
}
double fact(int n)
{
double sum = 0;
for(int i = 1; i
How many consecutive ones are there at the end of 1000
1+2+3+4+5+…… +1000=（1+1000）×1000÷2
=500500
How many zeros are there at the end of the result?
Only a few factors of 5 in 1000 are required
1000/5=200
How many factors are there in 1000
1000/25=40
Find the factors of 125 in 1000
1000/125=8
Finally, 625 is still one
Therefore, the final 200 + 40 + 8 + 1 = 249
There are 249 zeros
Ask what you don't understand
Wing of thought: the factorial "1000!" of a thousand. How many zeros are there?
249
Formula:
When 0 < n < 5, f (n!) = 0;
When n > = 5, f (n!) = K + F (k!), where k = n / 5 (rounding)
f(1000!) = 200 + f(200!) = 200 + 40 + f(40!) = 240 + 8 + f(8!) = 248 + 1 + f(1) =249
Detailed process:
Problem description
Given the parameter n (n is a positive integer), please calculate the number of "0" at the end of factorial n
For example, 5! = 120, the number of "0" at the end is 1; 10! = 3628800, the number of "0" at the end is 2; 20! = 2432902008176640000, the number of "0" at the end is 4
Calculation formula
The calculation formula is given first, and then the derivation process is given
Let f (x) denote the number of "0" contained at the end of positive integer x, then:
When 0 < n < 5, f (n!) = 0;
When n > = 5, f (n!) = K + F (k!), where k = n / 5 (rounding)
problem analysis
Obviously, it is impossible to calculate the result of factorial and count the number of "0" at the end of factorial. Therefore, we must analyze it from its numerical characteristics. Next, we will analyze it from the perspective of factorization
Let's first consider the general case. For any positive integer, if we factorize it, then the "0" at the end of it must be decomposed into 2 * 5. Here, each "0" must correspond to a factor "5". But please note that the factor "5" does not necessarily correspond to a "0" in factorization of a number, because a factor "2" is needed to realize its one-to-one correspondence
Let's go back to the original question
Conclusion 1: for factorial n! Of N, if there is a factor "5", it must correspond to a "0" at the end of n
This conclusion is proved as follows:
(1) When n < 5, the conclusion is obvious
(2) When n > = 5, let n! = [5K * 5 (k-1) *... * 10 * 5] * a, where n = 5K + R (0
How many zeros are there after the factorial of 1000? How many zeros are there after the result of multiplying 1 to 1000?
Among the rest, there are 80 "5" 5 * 1,3,7,9,11,13,17,19 ··· among the rest, 16 are multiples of 25 but not multiples of 125, and 32 are contributed
RELATED INFORMATIONS
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