Thread: Help finding closed form of sum

Hello all. Can somebody please help with the intermediate steps here? I have reached the point given, but not sure how to advance to the final solution. Many thanks

that's all, that's a closed form.

don't know what you want to do further.

Sorry, I wanted to know the necessary steps I need to take to get it into the closed form, the first equation is where I got to, I have the solution but don't know how to get there :-)

ah okay then, can you prove that ?

if you can do that, then you're done. (This is a fact known as geometric sum.)

Many thanks, solved.