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Prove that 2 power n lessthan equal to n factorial lessthan equal to n power n?
Assume 2^k < k! for all n > k here n > 2, then 2^n = 2^(n - 1)*2 < (n-1)! * n = n! Done. Connie and John
Gaussian elimination in c?
#include<stdio.h> #include<stdlib.h> #include<math.h> #include<conio.h> void main(void) { int K, P, C, J; double A[100][101]; int N; int Row[100]; double X[100]; double SUM, M; int T; do { printf("Please enter number of equations [Not more than %d]\n",100); scanf("%d", &N); } while( N > 100); printf("You say there are %d equations.\n", N); printf("From AX = B enter elements of [A,B] row by row:\n"); for (K = 1; K <= N; K++) { for (J = 1; J <= N+1; J++) { printf(" For row %d enter element %d please :\n", K, J); scanf("%lf", &A[K-1][J-1]); } } for (J = 1; J<= N; J++) Row[J-1] = J - 1; for (P = 1; P <= N - 1; P++) { for (K = P + 1; K <= N; K++) { if ( fabs(A[Row[K-1]][P-1]) > fabs(A[Row[P-1]][P-1]) ) { T = Row[P-1]; Row[P-1] = Row[K-1]; Row[K-1] = T; } } if (A[Row[P-1]][P-1] 0) { printf("The matrix is SINGULAR !\n"); printf("Cannot use algorithm --- exit\n"); exit(1); } X[N-1] = A[Row[N-1]][N] / A[Row[N-1]][N-1]; for (K = N - 1; K >= 1; K--) { SUM = 0; for (C = K + 1; C <= N; C++) { SUM += A[Row[K-1]][C-1] * X[C-1]; } X[K-1] = ( A[Row[K-1]][N] - SUM) / A[Row[K-1]][K-1]; } for( K = 1; K <= N; K++) printf("X[%d] = %lf\n", K, X[K-1]); getch(); }
What does the k stand for billion or trillion?
K stands for thousand.
What is a grouping of k objects taken from a set of n elements?
A combination, of k objects from n.
1 plus 3 plus 5 plus 7n how will you do this program?
Print "Type the upper limit (n) ?" Input n K = -1 WHILE K < = n K = K + 2 Sum = Sum + K WEND Print "The sum of all odd numbers up to "; n; "is "; Sum
What does the N K stand for in the translators name N K Sandars the translator of the Epic of Gilgamesh?
Nancy Katherine
What does 'N' Stand for in the periodic table?
N stands for Nitrogen on the periodic table.
What does nok stand for in texting?
No One Knows N--no o--one k--knows
What could N 22 C to K stand for in the Diffney quiz 2009?
N22 Cork to
What does K stand for in K9 pipes and fittings?
what does K stand for in K( , K 12 and K 14 pipes and fittings
C program for displaying perfect numbers using nested loop?
for (n=1; n<1000; ++n) { for (sum=0, k=1; k<=n/2; ++k) if (n%k==0) sum += k; if (sum==n) printf ("%d\n", n); }
Pascal's triangle using q-basic?
You could just use the binomial theorem. Step through rows, n, and entries, k, and compute the Pascal's triangle value as n!/(k!*(n-k)!) You'll actually have better luck if you use the natural log of a factorial, then you can use laws of exponents to get: exp(log(n!/k!/(n-k)!)) = exp(log(n!)-log(k!)-log((n-k)!)) = exp(logfact(n)-logfact(k)-logfact(n-k)) which won't run into the integer overflow problems that a plain factorial function would have. To fill up a logfact array, something like this might work: while(i<maxn) logfact(i)=logfact(i-1)+log(i) i=i+1 Wend Be careful to initialize correctly, and watch your conversion between integers and doubles (probably have to do some rounding to your final answers).
How do you write it in numbers k is a function of n and 7 times n equals k?
k = f(n) = 7n
C program for optimal merge pattern?
#include<iostream.h> #include<conio.h> void main() { clrscr(); int i,k,a[10],c[10],n,l; cout<<"Enter the no. of elements\t"; cin>>n; cout<<"\nEnter the sorted elments for optimal merge pattern"; for(i=0;i<n;i++) { cout<<"\t"; cin>>a[i]; } i=0;k=0; c[k]=a[i]+a[i+1]; i=2; while(i<n) { k++; if((c[k-1]+a[i])<=(a[i]+a[i+1])) { c[k]=c[k-1]+a[i]; } else { c[k]=a[i]+a[i+1]; i=i+2; while(i<n) { k++; if((c[k-1]+a[i])<=(c[k-2]+a[i])) { c[k]=c[k-1]+a[i]; } else { c[k]=c[k-2]+a[i]; }i++; } }i++; } k++; c[k]=c[k-1]+c[k-2]; cout<<"\n\nThe optimal sum are as follows......\n\n"; for(k=0;k<n-1;k++) { cout<<c[k]<<"\t"; } l=0; for(k=0;k<n-1;k++) { l=l+c[k]; } cout<<"\n\n The external path length is ......"<<l; getch(); }
What does the k stand for in 103 K?
It would stand for 103 kilometres or 103 thousand
What does the K in K-complex stand for?
The K stands for Kinetochore.
Sum of 1 plus 2 plus 3 plus 4 plus .. plus n?
n(n+1)/2 You can see this from the following: Let x=1+2+3+...+n This is the same as x=n+(n-1)+...+1 x=1+2+3+...+n x=n+(n-1)+...+1 If you add the corresponding terms on the right-hand side of the two equations together, they each equal n+1 (e.g., 1+n=n+1, 2+n-1=n+1, ..., n+1=n+1). There are n such terms. So adding the each of the left-hand sides and right-hand sides of the two equations, we get: x+x=(n+1)+(n+1)+...+(n+1) [with n (n+1) terms on the right-hand side 2x=n*(n+1) x=n*(n+1)/2 A more formal proof by induction is also possible: (1) The formula works for n=1 because 1=1*2/2. (2) Assume that it works for an integer k. (3) Now show that given the assumption that it works for k, it must also work for k+1. By assmuption, 1+2+3+...+k=k(k+1)/2. Adding k+1 to each side, we get: 1+2+3+...+k+(k=1)=k(k+1)/2+(k+1)=k(k+1)/2+2(k+1)/2=(k(k+1)+2(k+1))/2=((k+2)(k+1))/2=(((k+1)+1)(k+1))/2=((k+1)((k+1)+1)/2
