In[]:=
ts[k_,n_]:=SumSin
iπ
n-1
2
(3/2+k),{i,1,
n-1
2
-1}
In[]:=
ts2[k_,n_]:=
Sin
π
2
(3/2+k)Sin
(
n-1
2
-1)π
n
2
(3/2+k)
Sin
π
n
2
(3/2+k)
In[]:=
N[ts[112,3]]
Out[]=
1.2483
In[]:=
N[ts2[112,3]]
Out[]=
1.2483
In[]:=
z3b1[m_,n_]:=
3
π
3n-3
2
Sum[
k+1
(-1)
Binomial[-3,k]ts[k,n],{k,0,m}]
In[]:=
z3b2[m_,n_]:=
3
π
3n-3
2
Sum[
k+1
(-1)
Binomial[-3,k]ts2[k,n],{k,0,m}]
In[]:=
N[z3b1[Infinity,3]]
Out[]=
1.32867-1.11022×
-16
10

In[]:=
N[z3b2[Infinity,3]]
Out[]=
ComplexInfinity
In[]:=
Block[{$MaxExtraPrecision=300000},N[z3b2[Infinity,3],20]]
Sum
:Sum does not converge.
N
:Internal precision limit $MaxExtraPrecision = 300000. reached while evaluating
1
64
3
π
∞
∑
k=0
1+k
(-1)
Binomial[-3,k]Csc
1
8
3
2
+kπSin
3
8
3
2
+kπSin
1
2
3
2
+kπ.
Out[]=
ComplexInfinity