Use the Sum of the First 9 Terms to Approximate $$\sum _ { n = 1 } ^ { \infty } \frac { 6 } { n ^ { 7 } + n ^ { 2 } }$$

Short Answer

Use the sum of the first 9 terms to approximate the sum of the following series.
$$\sum _ { n = 1 } ^ { \infty } \frac { 6 } { n ^ { 7 } + n ^ { 2 } }$$
Write your answer to six decimal places.