In[]:=
NSum[
n
(-1)
(
1/n
n
-1),{n,2,3}]
Out[]=
-0.028036
In[]:=
NSum[
n
(-1)
(
1/n
n
-1),{n,2,17}]
Out[]=
0.099055
In[]:=
CMRB=N[Sum[
n
(-1)
(
1/n
n
-1),{n,2,Infinity}]]
Out[]=
0.18786
In[]:=
LogPlotCMRB,
N-Sum
m
(-1)
m!
Derivative[m][DirichletEta][m],{m,2,x}+Limit[D[DirichletEta[m],m],m->1]
,
Sum[
n
(-1)
(
1/n
n
-1),{n,2,x}],{x,1,30},PlotRange->Sum[
n
(-1)
(
1/n
n
-1),{n,2,27}],.192,PlotLegends->Placed["Expressions",Below]
Out[]=
CMRB
N-
x
∑
m=2
m
(-1)
(m)
DirichletEta
(m)
m!
+
lim
m1
∂η(m)
∂m

x
∑
n=2
n
(-1)
(
1/n
n
-1)
""