Prove the following. 4+1+4^-1+4^-2...4^-k = 16/3-1/(3)(4^k)
The Attempt at a Solution
I confirmed the basis step and proceeded by changing the variable to n and adding n+1. I now have (16/3) - (1/(3)(4^k)) + (1/4^k+1) = 16/3 - (1/(3)(4^k+1)). In trying to get these even I have tried simplifying (that made a mess), adding and subtracting by (3)(12k), multiplying and dividing by 4^k+1 and a combination of these tactics. I just need some direction on how to proceed or to know if I am going about this completely wrong. Thank you.