Determine whether the sequence a
n
​
=
n
2

1
1

​
+
n
2

2
1

​
+⋯+
n
2

n
1

​
converges or diverges. If it converges, find the limit. Note ∑
i=1
k
​
i=
2
k(k+1)
​
Converges (y/n) : Limit (if it exists, blank otherwise):