Use the Sum of the First 10 Terms to Approximate $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ( \ln ( 2 n ) ) ^ { 4 } + 1 }$

Essay

Use the sum of the first 10 terms to approximate the sum of the series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ( \ln ( 2 n ) ) ^ { 4 } + 1 }$ . Estimate the error involved in this approximation.