1/((3n-1)(3n+2)) = (1/3)*(1/(3n-1) - 1/(3n+2))
Тогда
S = 1/3*(1/2-1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... - 1/(3n+2)) = 1/3 * (1/2 - 1/(3n+2)) = n/(6n+4)
Ответ S = n/(6n+4)
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1/((3n-1)(3n+2)) = (1/3)*(1/(3n-1) - 1/(3n+2))
Тогда
S = 1/3*(1/2-1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... - 1/(3n+2)) = 1/3 * (1/2 - 1/(3n+2)) = n/(6n+4)
Ответ S = n/(6n+4)