gas8 said:yeah thx, I used 2^(-n) when n is even and 2^-(n+1 ) when n is odd
A convergent series is a type of infinite series where the terms of the series approach a finite limit as the number of terms increases.
One example of a convergent series is the geometric series 1 + 1/2 + 1/4 + 1/8 + ..., which approaches a limit of 2 as the number of terms increases.
A series is convergent if the limit of its terms approaches a finite value, and divergent if the limit is infinite or does not exist.
Convergent series are important in mathematics because they allow for the manipulation and approximation of infinite processes, and are used in the development of many mathematical concepts and techniques.
Yes, convergent series can have negative terms as long as the absolute values of the terms still approach a finite limit. One example is the alternating series 1 - 1/2 + 1/4 - 1/8 + ..., which has a limit of 1/3.