What am I doing wrong with this partial sum formula? I have this series:$$\sum_{n=1}^\infty (1-\frac{7}{4^n})$$
So my strategy is to divide it into two formulas to try and get a geometric formula:$$\sum_{n=1}^\infty 1 - \sum_{n=1}^\infty \frac{7}{4^n}$$
The first sum equals 1 and I simplify the second sum to a geometric formula:$$1-\sum_{n=1}^\infty 7(\frac{1}{4})^n$$
So I plug that into the formula $\frac{a(1-r^n)}{1-r}$ and end up with$$1-\frac{7(1-(\frac{1}{4})^n)}{1-\frac{1}{4}}$$
I simplify that and get$$1-\frac{28(1-(\frac{1}{4})^n}{3}$$
So that's how I did it but when I type that in my calculator it doesn't match up with the answers I calculated manually. Can somebody tell me where I went wrong?

$$\sum_{n=1}^\infty 1 = \infty$$
not one.
You can also observe that 
$$\lim_n(1-\frac{7}{4^n})=1 \neq 0$$
therefore, the series is divergent.
