Question

Find the nth partial sum

Answer 1

\[\sum_{n=2}^{\infty} \ln (1 - \frac{ 1 }{ n ^{2} } ) = \ln(1-\frac{ 1 }{ 4 } ) + \ln(1 -\frac{ 1 }{ 9 } ) + \ln(1-\frac{ 1 }{ 16 } ) + \ln (1 -\frac{ 1 }{ 25 } )+ .....\]

Answer 2

find the nth partial sum \[S _{n}\] of the series and use it to determine whether the series is convergent or divergent