Answer
Divergent
Work Step by Step
Consider the series as a sum of two series $\Sigma_{n=1}^{\infty}(1-\dfrac{7}{4^n})=\Sigma_{n=1}^{\infty}1-\Sigma_{n=1}^{\infty}7(\dfrac{1}{4^n})$
Since, the first part of series $-\Sigma_{n=1}^{\infty}7(\dfrac{1}{4^n})$ converges because it a geometric series with common ratio $r=\dfrac{1}{4}$
But the second part of series $\Sigma_{n=1}^{\infty}1$ shows that is diverges by the n-th integral test.
Hence, the resultant series is divergent.
