A new computing method of limit of a special sequence 〖JB({〗xn〖JB)}〗=〖JB({〗〖KG*5〗f〖JB((〗〖SX(〗1p〖〗np+1〖SX)〗〖JB))〗+f〖JB((〗〖SX(〗2p〖〗np+1〖SX)〗〖JB))〗+…+f〖JB((〗〖SX(〗np〖〗np+1〖SX)〗〖JB))〗〖JB)}〗(p>0) was presented by the definition of derivative. The method is very effective to compute this type of sequences. And the limit of several difficult sequences is computed by using this method.