I tried rewriting it to 4^-n and then using the geometric series test 1/1-r
Which makes it to -1/3 convergence. I am not sure if its correct or not...
Since you have , you can rewrite it as . This is because 1 to any power is still 1.
Now, because your indexing starts at 1 instead of 0, we can subtract 1 and then add 1.
This will make the index start at 0. The adding one happens to the exponent so now we have . This can be written as .
Of course, so we just move that out side the summation.
Thus, you have a geometric series times 1/4 which is your a in the formula