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n
k=1
1
n+ik
n
k=1
n-ik
(n+ik)(n-ik)
n
k=1
n
n
2
+k
2
-i
n
k=1
k
n
2
+k
2


lim
n
A
n
lim
n
n
k=1
n
n
2
+k
2
lim
n
1
n
{
1
1+(
1
n
)
2
+
1
1+(
2
n
)
2
++
1
1+(
n
n
)
2
}
1
0
1
1+x
2
dx
4

lim
n
B
n
lim
n
n
k=1
k
n
2
+k
2
lim
n
1
n
{
1
n
1+(
1
n
)
2
+
2
n
1+(
2
n
)
2
++
n
n
1+(
n
n
)
2
}−
1
0
x
1+x
2
dx−
1
2
log2


ȥ