Partial Sums of Infinite Series - Page 3

Questions
  • Show that if #lim_(xrarrx_o) f(x) = 0# and #lim_(xrarrx_o) g(x) = 0# then #lim_(xrarrx_o) f(x)*g(x) = 0# ?
  • How do you write a sum in expanded form?
  • Is #f(x) =cscx-sinx# concave or convex at #x=pi/3#?
  • How do you find the n-th partial sum of a geometric series?
  • What is the sum of the series 1/1, 1/2, 1/3, ... 1/n and 1/1, 1/4, 1/9....1/n^2 where n is finite?
  • How do you find the sum of #1+1/5+1/7^2+1/7^3+1/7^9+...+1/7^n+...#?
  • What is the partial sum of ?
  • How do you find the 5-th partial sum of the infinite series #sum_(n=1)^oo1/(n(n+2)# ?
  • How do you find the sum of #Sigma (3^n+4^n)/5^n# from n is #[0,oo)#?
  • Given constants #a_0, a_1,... a_k# such that #a_0+a_1+...+a_k = 0#, how do you show that #lim_(n->oo) (a_0sqrt(n)+a_1sqrt(n+1)+a_2sqrt(n+2)+...+a_ksqrt(n+k)) = 0# ?
  • Does #sum_(n=1)^oo (ln n)/(n+2)# converge or diverge?
  • Is #sum_(n=1)^oo sin^2(1/n)# convergent or divergent?
  • Does #a_n = [n(n+1)^(1/2)]/(n+n*sqrt(n))# converge?
  • How do you evaluate the Riemann sum for f(x), 1≤x≤7 with three equal sub-intervals and taking the sample points to be the left endpoints when given a table?
  • Does #sum_1^oo (-1)^n-1[(8n)/(n^3 +1)^(1/3)# converge?
  • What is the interval of convergence of #sum (x^(2n) )/( (2n)! )#?
  • What is the interval of convergence of #sum ((-1)^n*x^n ) / (n^2+1) #?
  • What is the interval of convergence of #sum n^x #?
  • How do you prove this ? #sum_(n=1)^oo a_n# converges #-># #sum_(n=1)^oo a_n^2# converges
  • How do you find #\lim _ { n \rightarrow \infty } \frac { 2x ^ { 5} - 3x ^ { 2} } { 3x ^ { 5} - x ^ { 3} }#?