Consider the series ∑n=0∞54n. The sum of a series is defined as the limit of the sequence of partial sums, which means

(a) The n-th partial sum of the infinite series,

is

Multiplying both sides by 1/4 gives

Subtract this from and solve for :

(your solution is also correct)

(b) The infinite sum is equal to the limit of the n-th partial sum:

and the sum indeed converges to 20/3.

i believe the answer is d.

hope it you! : d