4 The sequence $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ is such that, for all positive integers $n$,

$$a _ { n } = \frac { n + 5 } { \sqrt { } \left( n ^ { 2 } - n + 1 \right) } - \frac { n + 6 } { \sqrt { } \left( n ^ { 2 } + n + 1 \right) }$$

The sum $\sum _ { n = 1 } ^ { N } a _ { n }$ is denoted by $S _ { N }$. Find\\
(i) the value of $S _ { 30 }$ correct to 3 decimal places,\\
(ii) the least value of $N$ for which $S _ { N } > 4.9$.

\hfill \mbox{\textit{CAIE FP1 2015 Q4}}