Ratio Test for Convergence of an Infinite Series - Page 4

Questions
  • Find the ratio of students who attended less than (H)/(2) hours of lectures ?
  • How do you use the ratio test to determine if #sum_{k=1}^∞ k^5 3^(-k)# converges?
  • What is the interval of convergence of #sum (3x-2)^(n)/(1+n^(2)) #?
  • What is #lim_(x->oo) (sqrt(x^3+x+1)-sqrt(x^3-1))# ?
  • Does the series #sum_(n=1)^oo((2n)/(n!))# converge or diverge?
  • Does the series #sum_(n=1)^oo((2^(n-1)3^(n+1))/n^n)# converge or diverge?
  • #sum_(n=1)^oo ((prod_(1->n)2n-1)/(prod_(1->n)2n))^r# for what values of #r# does the sum converge?
  • Prove that this converges to 0:#(prod_(k=1)^n(lambdak+a)/(lambdak+b)),0<=a<b,lambda>0,n=1,2,3......#?
  • Does the series #sum_{n=1}^oo (5n)^(3n)/(5^n+3)^n# diverge or converge?
  • By the ration test for series convergence or divergence?
  • How do we find the radius of convergence?
  • For which #x in RR# does the series P(x) converge and for which does it diverge? #P(x) = sum 1/n * x^(n+2)# And how do i show that the relation #P'(x) - 2*((P(x))/x) = x^2/(1-x)# is valid for the inner side of of the convergence intervall?