9. In this question you must show detailed reasoning. A sequence \(t _ { 1 } , t _ { 2 } , t _ { 3 } \ldots\) is defined by \(t _ { n } = 5 - 2 n\).
Use an algebraic method to find the smallest value of \(N\) such that $$\sum _ { n = 1 } ^ { \infty } 2 ^ { t _ { n } } - \sum _ { n = 1 } ^ { N } 2 ^ { t _ { n } } < 10 ^ { - 8 }$$