how was sparta finally able to defeat athens at the end of the peloponnesian war
Peloponnesian War The Peloponnesian War (431â€“404 BC) was an ancient Greek war fought by the Delian League led by Athens against the Peloponnesian League led by Sparta. Historians have traditionally divided the war into three phases. In the first phase, the Archidamian War, Sparta launched repeated invasions of Attica, while Athens took advantage of its naval supremacy to raid the coast of the Peloponnese and attempt to suppress signs of unrest in its empire. This period of the war was concluded in 421 BC, with the signing of the Peace of Nicias. That treaty, however, was soon undermined by renewed fighting in the Peloponnese. In 415 BC, Athens dispatched a massive expeditionary force to attack Syracuse in Sicily; the attack failed disastrously, with the destruction of the entire force, in 413 BC. This ushered in the final phase of the war, generally referred to either as the Decelean War, or the Ionian War. In this phase, Sparta, now receiving support from Persia, supported rebellions in Athens' subject states in the Aegean Sea and Ionia, undermining Athens' empire, and, eventually, depriving the city of naval supremacy. The destruction of Athens' fleet at Aegospotami effectively ended the war, and Athens surrendered in the following year. Corinth and Thebes demanded that Athens should be destroyed and all its citizens should be enslaved, but Sparta refused.
Lucius Accius Atreus featured the line oderint dum metuant ("let them hate, so long as they fear"), later an infamous motto of Caligula.
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.
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