Partial Sums of Infinite Series - Page 4

Questions
  • if #sum_1^∞a_n# converges then #sum_1^∞a_n^3 # converges. ?
  • We have string #f_n# with #f_(n+1)-f_n=3f_n#, and #f_n=-2^(2n-1)#. If #h_n=f_1+f_2+...+f_n# then #lim_(n->oo)h_n/h_(n+1)=#?
  • What is the value of #sum_(k = 0)^oo k^2/(k!)#?
  • Show that #sum x/2^x = 2# summation running 0 to infinity ?
  • #sum_(k=1)^oo (k!)/(3k)^k = # ?
  • Find the inverse laplace transforms of the following? # 1/(s^2+4s+13)^2 # and # 1/( (s^2+4)(s+1)^2 ) #
  • What are continued fractions for?
  • Prove these questions using Principle of Mathematical Induction ?
  • How do you solve this problem? Please explain step by step.
  • True or false? A series #oo# #sum_(n=1)alpha_n# is convergent if #lim_(n->oo)S_n# converges. ( #S_n# = nth partial sum)
  • What is the 11th partial sum of #sum_(i=1)^∞ -7i+22#?
  • Is the series convergent or divergent?
  • Given that ∑Ur =5/6 - (1/n+2) - (1/n+3).i found that sum of infinity of ∞∑Ur is 5/6....but how to find sum of infinity of ∞∑ (Ur+1 + 1/(2∧r))?the answer given is (19/12)?
  • What is the interval of convergence of #sum2^n * x^n#?
  • What is the interval of convergence of #sum (-1)^n * (x^n/n) #?
  • How do you find #\lim _ { x \rightarrow \infty } \frac { x ( x + x ^ { 3} ) + 4x ^ { 4} } { 1- 2x ^ { 4} }#?
  • What is #lim x-> ∞# of #(2x^2-7)/(5x^2+x-3)#?
  • What is #sum_(n=1)^oo 1/(sqrt(n)+sqrt(n+1))# ?
  • Find the #lim_(x to pi/4) {4sqrt3-(cos(x)+sin(x))^5}/(1-sin(2x))#?
  • What is the interval of convergence of #sum (2+2/n)^n((x-1)/2)^n#?