How do I show that this sequence satisfies the given recurrence relation?

I have been stuck on this problem all day, so something is clearly not clicking. It's an example problem with a given solution, but I am totally lost Let c0,c1,c2,... be defined by the formula c subscript n = 2^n - 1 for all integers n ≥ 0. Show that this sequence satisfies the recurrence relation b... show more I have been stuck on this problem all day, so something is clearly not clicking. It's an example problem with a given solution, but I am totally lost

Let c0,c1,c2,... be defined by the formula c subscript n = 2^n - 1 for all integers n ≥ 0.

Show that this sequence satisfies the recurrence relation

b subscript k = 4b subscipt k-1

I apologize for the poor formatting

Eventually, it gets to c subscript k-1 = 2^k-1 -1 and I have no idea how
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