Limit Comparison Test for Convergence of an Infinite Series - Page 6

Questions
  • How do you find the limit of #\lim _ { n \rightarrow \infty } \frac { n + 2} { 3( n + 1) }#?
  • How to find #lim(ln(2x)/(2+x)) x-> # infinity?
  • How do you prove if #lim_(n->infty) x_(2n) = L = lim_(n->infty) x_(2n+1)#, then #lim_(n->infty) x_n = L#?
  • What is #lim_(x->oo) sqrt(x^2+1)/(x+1)# ?
  • Why does #lim_(x->+-oo) f(x) = lim_(x->0) f(1/x)#?
  • How do I calculate the limit of x-√x? where x is nearing to infinity
  • How do you show the equivalence of the two definitions of #e#, that is #lim_(n->oo) (1+1/n)^n = sum_(k=0)^oo 1/(k!)# ?
  • Show that limit of #sqrt(x){sqrt(x+2)-sqrt(x)}=1# as x approaches to infinity?
  • Show that limit of #{(n+1)^(1/3)-n^(1/3)}=0# as x approaches to infinity?
  • Find the value of limit of {1+2+3+......to (3n+2)terms}/(n+1)^2 as n approaches to infinity?
  • Lim x-> infinity 7/((e^x)+2) evaluate ?
  • Prove the absolute convergence of the series?
  • How do you prove: #lim_(x->0) sin(x)/x = 1# without using l'hopital's rule (or the derivative of sin(x) at all)?
  • How to calculate the limit of #(ln2/2+ln3/3+...+lnn/n)/ln^2n# when #x->∞# ?
  • What is the limit of 1/(sqrt(x)) as it goes to infinity?
  • What is lim of x-> 1 for 1/log(x)?
  • Evaluate the following limits lim x tends to 0[√3+x – √5-x]/x^2–1?
  • How to solve limit x/e^x without using l'hospital rule?