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Sequences
14. Sequences & Series / Sequences / Problem 5
Problem 5

Let {an}={3,32,33,34,…} \{a_n\} = \(\left\)\{3, \(\frac{3}{2}\), \(\frac{3}{3}\), \(\frac{3}{4}\), \(\ldots\) \(\right\)\} and {bn}={3,0,32,0,33,0,34,0,…} \{b_n\} = \(\left\)\{3, 0, \(\frac{3}{2}\), 0, \(\frac{3}{3}\), 0, \(\frac{3}{4}\), 0, \(\ldots\) \(\right\)\} . Are the limits limn→∞an\(\displaystyle\[\lim\)_{n \(\to\]\infty\)} a_n and limn→∞bn\(\displaystyle\[\lim\)_{n \(\to\]\infty\)} b_n equal?