In[]:=
m=NSum[(-1)^n*(n^(1/n)-1),{n,1,Infinity},Method->"AlternatingSigns",WorkingPrecision->207];
In[]:=
d=114705489440921816400568391832103;a1=10539265076340778455746831348074621;a2=1315939211433987901830906252006812;a3=2238154781652703157536445225769983;a4=464968409472439567819541453580715;a5=1917024616230569159116802658552184;​​​​N
a1
10d
+
(a2Sqrt[2])
d
+
(a3Sqrt[5])
2d
+
(a46^(1/6))
d
-
(a5Pi)
d
-m
Out[]=
-9.93177×
-201
10