Since 64/3 = 21 + 1/3 > 21, I assume S is supposed to be the value of the infinite sum. So we have for some constants a and r (where |r | < 1),
Consider the k-th partial sum of the series,
Multiply both sides by r :
Subtract this from
:
Now as k goes to ∞, the r ᵏ term converges to 0, which leaves us with
which we can solve for a :
Meanwhile, the 3rd partial sum is given to be
Substitute a into this equation and solve for r :
Now solve for a :
It follows that