an=(n+1)/[n²(n+2)²]
=(1/4)(4n+4)/[n²(n+2)²]
=(1/4)[(n+2)²-n²]/[n²(n+2)²]
=(1/4)[1/n²- 1/(n+2)²]
Sn=a1+a2+...+an
=(1/4)[1/1²-1/3²+1/2²-1/4²+...+1/n²-1/(n+2)²]
=(1/4)[(1/1²+1/2²+...+1/n²)-(1/3²+1/4²+...+1/(n+2)²)]
=(1/4)[1/1²+1/2²-1/(n+1)²-1/(n+2)²]
=5/16 -1/[4(n+1)²] -1/[4(n+2)²]