How do you apply the ratio test to determine if #sum_(n=1)^oo 3^n# is convergent to divergent?

Question

1781 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-15T03:05:06

The series diverges.

The the #n#th term in the series is given by #a_n=3^n.#

The ratio test states that the series should be convergent if:

#lim_(n->oo)a^(n+1)/a^n<1#

So, in our case we have:

#lim_(n->oo)3^(n+1)/3^n=lim_(n->oo)3^(n+1-n)=#

#=lim_(n->oo)3=3#

#3gt1# so the ratio test tells us this series diverges.