Find the limit of the sequence an=2^n/(2n-1)?

1 Answer
Apr 11, 2018

#lim_(n->oo)2^n/(2n-1)=oo#

Explanation:

So, we want #lim_(n->oo)2^n/(2n-1)=oo/oo#

This is an indeterminate form and does not tell us anything of value.

We could solve by applying l'Hospital's Rule, but a sequence is not differentiable, so we need to define a function in terms of #x.#

Let #f(x)=2^x/(2x-1)#

Then, differentiating numerator and denominator, we obtain

#lim_(x->oo)2^x/(2x-1)=lim_(x->oo)(2^xln(2))/2=oo/2=oo#

Thus,

#lim_(n->oo)2^n/(2n-1)=oo#

The sequence diverges to #oo#