(Solved): For the following telescoping series, find a formula for the nth term of the sequence of partial su ...

For the following telescoping series, find a formula for the $n$th term of the sequence of partial sums $\left\{S_n\right\}$. Then evaluate lim $S_n$ to obtain the value of the series or state that the series diverges. ${?}_{k=1}^{?}\left(\frac{3}{\sqrt{k+2}}?\frac{3}{\sqrt{k+4}}\right)$ ${\mathrm{S}}_n=$ (Type an exact answer, using radicals as needed.) Select the correct choice and fill in any answer boxes in your choice below. A. ${?}_{k=1}^{?}\left(\frac{3}{\sqrt{k+2}}?\frac{3}{\sqrt{k+4}}\right)=$ (Type an exact answer, using radicals as needed.) B. The series diverges,