according to the zhou the shang kings had lost their mandate of heaven because
Mandate of Heaven The prosperous Shang dynasty saw its rule filled with many outstanding accomplishments. Notably, the dynasty lasted for a considerable time during which 31 kings ruled over an extended period of 17 generations. During this period, the dynasty enjoyed a period of peace and tranquility in which citizens could make a good living. The government was originally able to control most of its internal affairs due to the firm support provided by the people. As time went on, however, the rulers' abuse of the other social classes led to social unrest and instability. The corruption in this dynasty created the conditions necessary for a new ruling house to rise â€”the Zhou dynasty. Rebellion against the Shang was led by Zhou Wu. They created the Mandate of Heaven to explain their right to assume rule and presumed that the only way to hold the mandate was to rule well in the eyes of Heaven. They believed that the Shang ruling house had become morally corrupt, and that the Shang leaders' loss of virtue entitled their own house to take over. The overthrow of the Shang Dynasty, they said, was in accordance with the mandate given by Heaven.[4]
Mandate of Heaven The concept of the Mandate of Heaven was first used to support the rule of the kings of the Zhou dynasty (1046–256 BCE), and legitimize their overthrow of the earlier Shang dynasty (1600–1069 BCE). It was used throughout the history of China to legitimize the successful overthrow and installation of new emperors, including non-Han ethnic monarchs such as the Qing dynasty (1636–1912). This concept was also used by monarchs in neighboring countries like Korea and Vietnam.[3]
Zhou dynasty K.E. Brashier writes in his book "Ancestral Memory in Early China" about the tsung-fa system of patrilineal primogeniture: "The greater lineage, if it has survived, is the direct succession from father to eldest son and is not defined via the collateral shifts of the lesser lineages. In discussions that demarcate between trunk and collateral lines, the former is called a zong and the latter a zu, whereas the whole lineage is dubbed the shi. [...] On one hand every son who is not the eldest and hence not heir to the lineage territory has the potential of becoming a progenitor and fostering a new trunk lineage (Ideally he would strike out to cultivate new lineage territory). [...] According to the Zou commentary, the son of heaven divided land among his feudal lords, his feudal lords divided land among their dependent families and so forth down the pecking order to the officers who had their dependent kin and the commoners who "each had his apportioned relations and all had their graded precedence""[31]
1 + 2 + 3 + 4 + ⋯ which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.