The discussion focuses on proving the divergence of the sequence defined by the expression (n^2 + 1)/n as n approaches infinity. The limit of this sequence is confirmed to be infinity, establishing that it diverges. A formal proof involves demonstrating that for any large positive number M, there exists a number N such that for all n ≥ N, the sequence terms a_n exceed M. This is achieved by solving the inequality (n^2 + 1)/n > M to find an appropriate N.
PREREQUISITESStudents of calculus, mathematicians, and educators seeking to understand or teach the formal proofs of sequence divergence.
transgalactic said:i got (n^2+1)/n
when n->infinity the limit is infinity.
what is the formal proof that a sequence diverges ?