Difficulty to understand the value of a sum

I am trying to understant the formula below, it is part of bigger exercise but I am stack on this partiular one:

Sum from k=v+1 to n of (1/ (1/v+1)^(k-v-1)) = (1-(1/(v+1))^(n-v))/1-1/(v+1)

where v<n

This is in latex:

\sum_{k=v-1}^{n}\frac{1}{(v+1)^{k-v-1}}=\frac{1-(\frac{1}{v+1})^{n-v}}{1-\frac{1}{v+1}}

Thank you in advance!

Sorry for latex, I am trying about 2 hours now.. The code produced from the buttons below doesn't work, the code in the latex forum doesn't work either, so I removed the math tags. Image upload does not work too, sorry!