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  1. K

    Prove that none of them is prime

    i don't know, im confused!
  2. K

    Prove that none of them is prime

    you would start at n! + 1,000,003 ?
  3. K

    Prove that none of them is prime

    So there are n-2 consecutive non-primes starting with n! ?
  4. K

    Prove that none of them is prime

    ok, so a factor of n!+3 is 3, and a factor of n!+2 is 2 and so on. So a factor of n!+n is n. This shows that none of them is prime. How would i go about doing the second part of the question?
  5. K

    Prove that none of them is prime

    Is (n factorial + 2) a factor of it? Which would then apply to the others, which would show that none of them were prime. For them each to be prime, their only factors would have to be themselves and 1.
  6. K

    Prove that none of them is prime

    Homework Statement Let n be a part of the natural numbers, with n>=2. Consider the numbers [n factorial +2 ], [n factorial + 3], ..., [n factorial + n]. Prove that none of them is prime, and deduce that there are arbitrarily long finite stretches of consecutive non-prime nummbers in the...
  7. K

    Fermat's little theorem

    This is ok if p doesnt divide n, but the question asks me for all integers n. So how do i show it's also true for when p divides n?
  8. K

    Fermat's little theorem

    sorry, silly mistake. dividing by n would give me, n^(p-1) equivalent to 1 (mod p) which is fermat's little theorem. so is this all i need to do?
  9. K

    Fermat's little theorem

    ok, so in my question, c=n ? So by dividing by n i would get, 1^p is equiavlent to 1 (mod p) How do i reach n^(p-1) on the left hand side?
  10. K

    Fermat's little theorem

    Homework Statement From fermat's little theorem deduce that when p is prime, n^p is equivalent to n (mod p) for all integers n. Homework Equations The Attempt at a Solution I know from Fermat's Little Theorem that , n^(p-1) is equivalent to 1 (mod p), but i don't...
  11. K

    L'hopitals rule?

    yea, thank you!
  12. K

    L'hopitals rule?

    Homework Statement Find the limit of f(x)=[xcosx]/[x^3 + 1] as x tends to infinity. Homework Equations The Attempt at a Solution Can i use l'hopitals rule here? Or if not, what are the conditions for f(x) to meet so that i may use l'hopitals rule? Without using l'hop i know...
  13. K

    Converging series

    Homework Statement Show that the following series converges: Homework Equations Sum of (from n=1 to infinity) of [3^n + 4^n] / [3^n + 5^n] The Attempt at a Solution Some help on this question would be much appreciated as i really don't know how to start it. Thanks
  14. K

    Complex Integration

    Homework Statement Evaluate the following intergral: Homework Equations Intergral from gamma of (y)dz, where gamma is the union of the line segments joining 0 to i and then i to i+2 The Attempt at a Solution I have no idea how to do this!
  15. K

    Open sets

    Homework Statement For the following set, state and justify whether or not it is open or closed. Homework Equations A={z| Im z >1} The Attempt at a Solution I know the definition of an open set, but im not sure how to use it to solve this question.
  16. K

    Derivative of function

    Homework Statement Compute the derivative of the following function. Homework Equations f:[1,-1] arrow [-pie/2, pie/2] given by f(x)=sin^-1 (x) The Attempt at a Solution I know that f ' (x)=1/[sqrt(1-x^2)] Im not sure how to include the intervals of pie given, not sure what...
  17. K

    Discussing continuity of a function

    Homework Statement Discuss the continuity of the function f defined for all x belongs to [0,1] by f(x)=x if x is rational and f(x)=x^2 is x is irrational. Homework Equations The Attempt at a Solution I have no idea how to begin this question.....some help would be great thanks!
  18. K

    Limit, as x tends to 0

    Homework Statement Does f(x) tend to a limit as x tends to 0? Homework Equations f(x)=[sinx]/[x^2] The Attempt at a Solution Well i sinx would tend to zero and so would x^2, so would the limit just be zero?
  19. K

    Converging series

    i know for the comparison test, you assume that a(n)<= k.b(n) Then if b(n) is convergent, a(n) is also convergent. However i still dont see how i can get my series to be <= to a constant times another series.
  20. K

    Converging series

    Homework Statement Show that the following series converges: Homework Equations Sum of n=1 to n=infinity of [(n+1)/(n^2 +1)]^2 The Attempt at a Solution I thought about using the ratio test, so if the limit as n tends to infinity of a(n+1) / a(n) < 1, then a(n) - the series - would...
  21. K

    Sequence infinity proof

    Homework Statement Prove that the following sequence (a(n)) has the property that a(n) tends to infinity as n tends to infinity. Homework Equations a(n)=[n+7]/[2+sin(n)] The Attempt at a Solution i tried l'hopitals rule, so i got 1/cos(n).....which wouldnt work. so im not sure...
  22. K

    Runge-kutta formula

    How do i find what k(1) - k(4) is? Do i substitute anything in for h? Also what are the value for t(i) and y(i)?
  23. K

    Runge-kutta formula

    thankyou very much for that....i understand all of what you have said. So i found for my equation that f[t(0),y(0)] = 1, since y'=y and y(0)=1 Im still slightly confused as to how to find y(h)?
  24. K

    Runge-kutta formula

    Homework Statement Use the fourth order Runge-Kutta formula to advance the differential equation: dy/dt = y with y(0)=1 forward one step h. That is find y(h). Homework Equations The Attempt at a Solution The Runge-Kutta formula is: x(i+1)=x(i)+h/6 [k(1)+2k(2)+2k(3)+k(4)]...
  25. K

    Supremums and infimums

    Homework Statement Show that for all x,y in R (real numbers), sup{x,y}=1/2(x+Y+|X-Y|), and inf{x,y}=1/2(X+Y-|x-y|) Homework Equations The Attempt at a Solution i know that the supremum is the lowest upper bound and that the infimum is the largest lower bound. However i really...
  26. K

    Proof by induction

    thanks for the help!
  27. K

    Proof by induction

    Homework Statement Define the numbers a(0),a(1),a(2),...by a(0)=1, a(1)=3, a(n)=4[a(n-1) - a(n-2)]. for n>=2 Show by induction that for all n>=1, a(n)=2^(n-1) [n+2] Homework Equations The Attempt at a Solution proof by induction is not my stong point, and i really don't know where to...
  28. K

    Proof by induction

    Homework Statement Show that (n+1)^4 < 4n^4 whenever n >= 3 Homework Equations The Attempt at a Solution I need to prove this by induction, so i assume it is true and then prove that when n=n+1 it is also true. so it would become (n+2)^4 < 4(n+1)^4 Im not sure how to...
  29. K

    Supremums 'alpha' and 'beta' problem

    Well the definition of supremum is that it's the least upper bound, it is greater than or equal to each element in the set. I still don't know how so start off showing that alpha+beta is the sup of A+B...
  30. K

    Supremums 'alpha' and 'beta' problem

    Homework Statement Let A, B,be two non empty sets of real numbers with supremums 'alpha' and 'beta' respectively, and let the sets A+B and AB be defined by: A+B={a+b / a belongs to A, b belongs to B}, AB= {ab / a belongs to A, b belongs to B}. Show that alpha+beta is a supremum of A+B...
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