Question

i need to show whether the series is convergent or divergent by expressing Sn as a telescoping sum. \[\sum_{1}^{\infty}2\div \left( n ^{2}+4n+3 \right)\]

Answer 1

You need to be able to split the poly as two separate sums where majority of terms will cancel.

The above conveniently divides into 1/(n+1) - 1/(n+3) for this purpose.