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Why is the sum of the reciprocals of all of the divisors of a perfect number equal to 2?
Suppose N is a perfect number. Then N cannot be a square number and so N has an even number of factors.Suppose the factors are f(1) =1, f(2), f(3), ... , f(k-1), f(k)=N.Furthermore f(r) * f(k+1-r) = N for r = 1, 2, ... k so that f(r) = N/f(k+1-r)which implies that 1/f(r) = f(k+1-r)/NThen 1/f(1) + 1/(f(2) + ... + 1/f(k)= f(k)/N + f(k-1)/N + ... + f(1)/N= [f(k) + f(k-1) + ... + f(1)] / N= 2N/N since, by definition, [f(k) + f(k-1) + ... + f(1)] = 2N
What is the rule to the pattern 1 3 7 15 31?
its Mersenne's Number f(n)= (2^n) -1 where n is the number of sequence. so f(1) = 1 f(2) = 3 f(3) = 7 f(4) = 15 f(5) = 31 ...
What describes the sequence 1 1 2 3 5 is it arithmetic or geometric?
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
What is infinity divided by 5?
Infinity divided by any finite number is infinity. Here are the rules: 1. Infinity divided by a finite number is infinite (I / f = I); 2. Any finite number divided by infinity is a number infinitesimally larger than, but never equal to, zero (f / I = 1 / I); 3. Infinity divided by infinity is one (I / I = 1), or in fact any other positive number (I / I = and so on...); 4. Infinity multiplied by zero (no infinity) is zero (I * 0 = 0); 5. Infinity divided by a positive finite number is infinity (I / +f = I); 6. Infinity divided by a negative finite number is minus infinity (I / -f = -I); 7. Infinity divided by zero is not possible; 8. Infinity plus infinity is infinity (I + I = I); 9. Zero divided by infinity (nothing divided into infinity) equals zero (0 / I = 0); 10. Infinity plus a finite number is infinity (I + f = I); 11. Infinity minus a finite number is infinity (I - f = I); but 12. Infinity minus infinity, due to the nature of infinity, can be zero, infinity, or minus infinity (I - I = -I, 0, I).
What is oilers number?
You are referring to Euler's number. It is pronounced like "eh-uh-le-uh" because the name is German. Euler's number is the number e, which is the base of the natural logarithm. The number e is extremely prominent in any mathematical endeavour involving calculus in any way, as it has many useful properties. For example, the derivative of the function f(x) = e^x is the function df(x) = e^x = f(x). It is the only function that has this property. The natural logarithm is itself also very useful. It was discovered by studying properties of the integral of the function f(x) = 1/x, which did not have any closed form antiderivative in terms of the elementary functions of that time period, even though g(x) = x^n had the simple antiderivative Ig(x, C) = (x^(n+1))/(n+1) + C for any real n except n = -1. It was eventually discovered that the function f(x) defined as the definite integral of f(t) = 1/t from t = 1 to t=x had the properties of a logarithmic function with base e. e is transcendental, so it is both irrational and is not the root of any polynomial function with rational coefficients. Or in simple words 2.718281828459
Algorithm to find prime numbers below ten?
Take each number in turn, call it "n", and check whether it has any factors f, such that 1 < f < n. If it doesn't, it is a prime number.Take each number in turn, call it "n", and check whether it has any factors f, such that 1 < f < n. If it doesn't, it is a prime number.Take each number in turn, call it "n", and check whether it has any factors f, such that 1 < f < n. If it doesn't, it is a prime number.Take each number in turn, call it "n", and check whether it has any factors f, such that 1 < f < n. If it doesn't, it is a prime number.
The product of 11 and a number?
(11)f
Factorial number's summation's program upto n numbers in c language?
#include#includeint a,f,n,sum=0; printf("Enter any number"); scanf("%d",&n); f=1; for(a=1;a<=n;a ); { f=f*a; } for(f=1;f<=n;f ); { sum=sum f; } printf("sumation of factorial numbers :",sum); getch(); }
Is the number 1 prime or composite?
.1 is not prime, since a prime has exactly two positive divisors.1 is not composite since it cannot be written as the product of primes.The number 1 is not called a prime OR composite number. It is called a f*cking UNIT !
What is the limitation to the domain of a function?
Any number that produces an undefined result from a function f(x) is not in its domain.For example, the number 0 is not in the domain of f(x) = 1/x, because 1/0 is undefined.Undefined answers will result from any of the following situations:- Dividing by 0- Taking the square root of a negative number- Taking the log (any base) of 0 or any negative number- Taking the log (base 1) of any number
Why is the sum of the reciprocals of all of the divisors of a perfect number equal to 2?
Suppose N is a perfect number. Then N cannot be a square number and so N has an even number of factors.Suppose the factors are f(1) =1, f(2), f(3), ... , f(k-1), f(k)=N.Furthermore f(r) * f(k+1-r) = N for r = 1, 2, ... k so that f(r) = N/f(k+1-r)which implies that 1/f(r) = f(k+1-r)/NThen 1/f(1) + 1/(f(2) + ... + 1/f(k)= f(k)/N + f(k-1)/N + ... + f(1)/N= [f(k) + f(k-1) + ... + f(1)] / N= 2N/N since, by definition, [f(k) + f(k-1) + ... + f(1)] = 2N
What is the oxidation number of IF?
oxidation number of I is -1. oxidation number of F is +1.
What is the oxidation number for the f element?
In compounds fluorine, F, has an oxidation number of -1.
What is the H.C. F. of two distinct prime number?
The GCF of any set of distinct prime numbers is 1.
What is the rule to the pattern 1 3 7 15 31?
its Mersenne's Number f(n)= (2^n) -1 where n is the number of sequence. so f(1) = 1 f(2) = 3 f(3) = 7 f(4) = 15 f(5) = 31 ...
What describes the sequence 1 1 2 3 5 is it arithmetic or geometric?
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
What is the domain of the function of fx5x?
f(x)=5x Domain is any number for x that will provide a real number for f(x). In this function, x can be any real number, and f(x) will be a real number. Thus domain is all real numbers.
