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\noindent {\bf Problem statement} Suppose $A$ and $B$ are positive
numbers. Decide whether the following sequences converge. If they
converge, try to find their limits. Your answers
may involve both numbers and their relationship. 

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\noindent a) $c_n= \root n \of {A^n + B^n}$\qquad\qquad b) $d_n= \root n \of
{A^n + B}$

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\noindent {\bf Hint} Experiment! Choose various values of $A$ and $B$
and compute the first five or ten terms of each sequence. Then verify
your guesses in general with algebra and calculus.









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