Given the infinite series
a)show that the series is a geometric series
b)determine the set of value of so that the sum to infinity , exist
c)if , find the sum of the first five terms, and .Show that
This problem is solved in a standard way, so you need to show some effort.
converges iff . When you are looking for the set of x for which the series converges, remember that an equality changes sign when multiplied by a negative number.
For part (a), study the definition of geometric progression and geometric series.
For part (b), I gave you a hint. I used the term "converges." By definition, a series converges iff its sum to infinity exists.