how to derive formula for the sum of a series

[slapshot136]

so I have a series that looks like this:

r^0 + r^2 + r^4 + r^6 + ... r^2n = ?

how can I derive a formula for what the sum is equal to?

similar example:

r^0 + r^1 + r^2 + r^3 + ... r^n = (r^(n+1)-1) / (r-1)

Thanks for any help

 

[HallsofIvy]

How about \(\displaystyle (r^2)^0+ (r^2)^1+ (r^2)^2+ (r^2)^3+ \cdot\cdot\cdot+ (r^2)^n\)?

 

[slapshot136]

How about \(\displaystyle (r^2)^0+ (r^2)^1+ (r^2)^2+ (r^2)^3+ \cdot\cdot\cdot+ (r^2)^n\)?

that would be exactly what I am looking for, thanks!