Geometric Series - Page 3

Questions
  • Using the first 10 terms graph the sequence, and use the graph to discuss the convergence or divergence of the sequence an=3-1/2^n?
  • Write the nth term of the sequence -1/2,1/3,-2/9,4/27,-8/81?
  • For what r does #3/(n^(2r - 3))# converge or diverge?
  • How to use the formula for the sum of a geometric series to find the sum or state that the series diverges ?
  • How to find the infinite sum ?
  • For what r does #3/(n^(2r - 3))-3/n# converge or diverge?
  • How do you evaluate #\sum _ { n = 1} ^ { \infty } \frac { ( - 3) ^ { n - 1} } { 7^ { n } }#?
  • Determine whether the series converge or diverge?
  • How do you test #\sum _ { m = 1} ^ { \infty } \frac { ( - 6) ^ { m + 1} } { 4^ { 8m } }# for convergence or divergence?
  • What is #sum_(n=0)^oo (1/5^n + 1/9^n)# ?
  • Does #sum_(n=2)^oo 6/(n^2+3)# converge or diverge ?
  • Find the limit of the sequence or why it diverges?
  • Prove by mathematical induction? #n + 3 < 5n^2 \ \ AA n >= 1 #
  • #2n - 4 <= 2^(n-3)#, for #n >= 6#. Help me to prove this mathematical induction please?
  • #lim_(n->oo)((4*n^2 + 6*n + 3)/(4*n^2 + 7*n - 2))^(7*n + 5) = # ?
  • Does this geometric series converge or diverge?
  • How can I find the Sum of #5-10/3+20/9-40/27+80/81-#... ?
  • How does #g(t) = 9^t# change over the interval from #t=5# to #t=7#?
  • Is #sum_(n->0)^oo g_n(x)# with #g_n(x) = arctan(\frac{2x}{x^2+n^3})# continuous ?
  • Kindly sum this series , if its convergent and state why its convergent?