Let a_{n} is the following.
(a) Determine whether {a_{n}} is convergent.
(b) Determine whether is convergent.
Also the answer to be is that it is not convergent, but why????????
a) Divide all parts of the fraction by the dominant term (the term that increases fastest when n increases). Then see what happens when n tends to infinity.
b) The infinite sum can only converge if a_{n} is a null sequence.
Haha Plato replied less than a minute before me.
So for (b), your series diverges since the terms do not approach zero (you will show in part (a) that they approach a different number). Some textbooks call this the Divergence Test.
I hope that clarifies Plato and Shakarri's answer a little.
- Hollywood