Answer: The given series neither converges nor diverges.
Step-by-step explanation: We are given to determine whether the following series converges or diverges :
If the series converges, we are to find its sum.
The given series can be written as :
We note that the given series is a geometric one with first term 1 and common ratio given by
We know that a geometric series with common ratio r converges if |r| <1 and diverges if |r| > 1.
Since |r| = 1 for the given series, so the series will neither converge nor diverge.
Thus, the given series neither converges nor diverges.
A 4th degree polynomial will have at most 3 extreme values. Since the degree is even, there will be one global extreme, with possible multiplicity. The remainder, if any, will be local extremes that may be coincident with each other and/or the global extreme.
(The number of extremes corresponds to the degree of the derivative, which is 1 less than the degree of the polynomial.)
