f[r_]:=-2N[Sum[1/12(2+2n-Sqrt[2(5+2n(2+n)+4Cosh[2r]+Cosh[4r])])Sech[r]^4Tanh[r]^(2n),{n,0,∞}]]​​​​​​Plot[f[x],{x,2.4,2.6},ImageSize600]​​
NSum
:Summand (or its derivative)
1
12
2+2n-
2
5+2n(2+n)+4Cosh[Times[2]]+Cosh[4x]

4
Sech[x]
2n
Tanh[x]
is not numerical at point n = 46661.
NSum
:Summand (or its derivative)
1
12
2+2n-
2
5+2n(2+n)+4Cosh[Times[2]]+Cosh[4x]

4
Sech[x]
2n
Tanh[x]
is not numerical at point n = 46661.
NSum
:Summand (or its derivative)
1
12
2+2n-
2
5+2n(2+n)+4Cosh[Times[2]]+Cosh[4x]

4
Sech[x]
2n
Tanh[x]
is not numerical at point n = 46661.
General
:Further output of NSum::nsnum will be suppressed during this calculation.
Plot
:{Tanh[x]-0,(5+2n(2+n)+4Cosh[2x]+Cosh[4x])-0,Cosh[x]-0,Im[Tanh[x]]-0,Im[2n(2+n)+4Cosh[2x]+Cosh[4x]]-0} must be a list of equalities or real-valued functions.
2.45
2.50
2.55
2.60
0.42
0.43
0.44
0.45
0.46
0.47
0.48