For a geometric series explain how you can tell if the series converges or diverges as you keep adding an infinite number of terms to the series. be sure that your explanation is clear on what it means to converge or diverge. show using an example(s).

It will converge if the common factor  r  is between 0 and 1.
For example:-
 A GS with  first term a1 = 2  and d = 1/2,   the  terms are:-

2 , 1 , 1/2, 1/4, 1/8,1/16 and so on

Each term gets smaller and smaller and they will become very small - close to 0.   The sum will converge to a certain value also.
In this case it will converge to  2 /( 1 - 1/2) = 4

If d > 1  the terms will increase without bounds and the sum gets bigger and bigger . The series  diverges.

for example  2, 8, 32, 128, 512   where a1 = 2 and d = 4.

Iwould say rat and vsu but i’m not 100% sure

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)