6. A geometric series has first term 5 and common ratio \(\frac { 4 } { 5 }\).
Calculate
- the 20th term of the series, to 3 decimal places,
- the sum to infinity of the series.
Given that the sum to \(k\) terms of the series is greater than 24.95,
- show that \(k > \frac { \log 0.002 } { \log 0.8 }\),
- find the smallest possible value of \(k\).