- In this question you must show detailed reasoning.
A sequence \(t _ { 1 } , t _ { 2 } , t _ { 3 } \ldots\) is defined by \(t _ { n } = 25 \times 0.6 ^ { n }\).
Use an algebraic method to find the smallest value of \(N\) such that
$$\sum _ { n = 1 } ^ { \infty } t _ { n } - \sum _ { n = 1 } ^ { N } t _ { n } < 10 ^ { - 4 }$$