Find the infinite sum (if possible.)

1. $8 - 6 + \frac { 9 } { 2 } - \frac { 27 } { 8 } + - \dots$

   Hint (a):

   Treat as the sum of two different sums.

   Hint 2 (a):

   $t(n)=\frac{128}{9}\left(\frac{9}{16}\right)^n$

   $u(n)=-\frac{32}{3}\left(\frac{9}{16}\right)^n$

   More Help (a):

   Use the geometric summation formula on both and add the results.

2. $\sum _ { k = 0 } ^ { \infty } \frac { 1 } { 8 } ( 2 ) ^ { k }$

   Hint (b):

   Remember the prerequisites of the summation formula.