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## Main Question or Discussion Point

I am going through Olivier Kahn's book "Molecular Magnetism". I am stuck on something that seems so simple. On page 10, it is stated that

[tex]\chi=C\sum_{M_S=-S}^{+S}\frac{{M_S}^2}{2S+1}[/tex]

The book then states that this leads to

[tex]\chi=\frac{C}{3}S(S+1)[/tex]

I've tried to figure the steps between but I can't get anywhere. What am I missing here?

EDIT: Of course, [tex]M_S=-S,-S+1,...,S-1,S[/tex]

PS. [tex]C=\frac{Ng^2\beta^2}{kT}[/tex] where [tex]\beta[/tex] is the Bohr magneton and [tex]k[/tex] is the Boltzmann constant.

[tex]\chi=C\sum_{M_S=-S}^{+S}\frac{{M_S}^2}{2S+1}[/tex]

The book then states that this leads to

[tex]\chi=\frac{C}{3}S(S+1)[/tex]

I've tried to figure the steps between but I can't get anywhere. What am I missing here?

EDIT: Of course, [tex]M_S=-S,-S+1,...,S-1,S[/tex]

PS. [tex]C=\frac{Ng^2\beta^2}{kT}[/tex] where [tex]\beta[/tex] is the Bohr magneton and [tex]k[/tex] is the Boltzmann constant.