If it were the case that then the interval of convergence is .
Thus something is amiss with the problem or the given answer.
Review the statement and remember given answers are often incorrect.
So, simply, where do I go wrong?
The question:
The interval of the power series is . Find .
My solution:
For the series to be convergent, d'Alemberts ratio test must be satisfied, i.e. must hold true.
For the series given we have:
.
This gives
It is easy to show that the series is convergent also for and (by making these substitutions into the series given).
So now we have that for the series to be convergent.
But the interval of convergence is , meaning that .
However, the key in my book claims the answer to be .
Thank you in advance
Aliquantus
Thank you for your reply, Plato. I just got another reply on a swedish forum, also saying that there is a typo in my book. The only strange thing is that they give the same, apparently wrong, answer in both the key and the solution manual. I suppose not even authors are perfect. Thanks again!