Two Identical Particles w/ Spin State s

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degerativpart
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what would the system of two identical paritcles with a spin, let's say s? I figure its different for symmetrical and anti-symmetrical spin states but how do you deal with the defined spin state s.
 
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How is 1 + 1 = 1?
The definition of an antisymmetric spin means that they are in different energy states.
S+1/S -- isn't this the ratio of symmetric to antisymm spins? How would you even begin to prove this?