I am trying to use "telescoping" demonstrated in this tutorial https://www.youtube.com/watch?v=lPCS2FFyqNA to solve this recurrence relation.
I started it off below, but quickly lost my way. Might anyone show the process for breaking down this recurrence relation, $ T(n) = 4T(n/4) + 5n$ into a closed form?
$T(n) = 4T(n/4) + 5n $
$T(n-1) = 4T((n-1)/4) + 5n - 5$
$T(n-2) = 4T((n-2)/4) + 5n - 10 $
$....$ $T(n) = ???$
I know we would cancel out the terms on the left and the right side of the $=$ but because it's divided by 4, I'm getting a bit lost...