\frac{3^k - 1 + 2*3^k}{2}
I will write it like this
\frac{1*3^k - 1 + 2*3^k}{2}
And then rewrite it like this:
\frac{1* 3^k + 2*3^k -1}{2}
From the numerator, if we have ONE lot of 3^k and we add it to TWO lots of 3^k, isn't that the same as saying THREE lots of 3^k?
\frac{3* 3^k-1}{2}...