## Multivariable Calculus, 7th Edition

$\Sigma^{\infty}_{n=1} \frac{1}{\ln (n+1)}$ $a_{n}=\frac{1}{\ln (n+1)}$ partial sum $s_{n} = a_{1} + a_{2} + ... +a_{n}$ $n=1$ $a_{1}=1.44270$ $s_{1}=1.4427$ $n=2$ $a_{2}=0.91024$ $s_{2}=2.3529$ $n=3$ $a_{3}=0.72135$ $s_{3}=3.0743$ $n=4$ $a_{4}=0.62133$ $s_{4}=3.6956$ $n=5$ $a_{5}=0.55811$ $s_{5}=4.2537$ $n=6$ $a_{6}=0.51390$ $s_{6}=4.7676$ $n=7$ $a_{7}=0.48090$ $s_{7}=5.2485$ $n=8$ $a_{8}=0.45512$ $s_{8}=5.7036$ The series appears to be divergent because it is not increasing to any particular number.