Asequence{an} is given by a1=sqrt(2), an+1=sqrt(2+an).
a) by induction or otherwise, show that {an} is increasing and bounded above by 3. apply the monotonic sequence theorem to show that lim n--> infinity an exists.
b) find lim n--> infinity an.

It is much safer to be feared than loved. . among the wonderful deeds of hannibal this one is enumerated: that having led an enormous army, composed of many various races of men, to fight in foreign lands, no dissensions arose either among them or against the prince, whether in his bad or in his good fortune. this arose from nothing else than his inhuman cruelty . . but without that cruelty, his other virtues were not sufficient to produce this effect. . that it is true his other virtues would not have been sufficient for him may be proved by the case of scipio, that most excellent man . . his army rebelled in spain; this arose from nothing but his too great forbearance, which gave his soldiers more license than is consistent with military discipline. –the prince, niccolò machiavelli which words in the passage have negative connotations?inhuman, cruelty, rebelled how do the words with negative connotations support the claim?by defining the actions of a leader who is to be feared