Finite Geometric Series : you use this formula

Geometric Series : {

Infinite Geometric series : Because Diverging r>1 or r<-1，so no sum

For example : t=-0.5, r=-3

So -0.5,1.5,-4.5,13.5. It gets bigger and it gets smaller, no fixed size,either keep getting bigger or you keep getting smaller.

Converging: you can use this formula -1<r<1 =a/1-r n= ∞