suppose A and B are positive numbers. Decide whether the following s.pdf

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The document discusses two sequences, a) Cn = (A^n + B^n)^(1/n) and b) dn = (A^n + B)^(1/n), where A and B are positive numbers. It asks to determine if the sequences converge and if so, find their limits, which may involve the relationship between A and B. It suggests finding the first few terms of each sequence as a hint.

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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. a) Cn = (A^n + B^n)^(1/n) b) dn = (A^n + B)^(1/n). fine the first five or ten terms
of the sequence is a hint given. a and B can have any values that you choose.
Solution
a) Cn = (A^n + B^n)^(1/n) converge C1 = (A + B) C2 = (A^2 + B^2)^(1/2) C3
= (A^3 + B^3)^(1/3) C4 = (A^4 + B^4)^(1/4) C5 = (A^5 + B^5)^(1/5) b) dn = (A^n +
B)^(1/n) converges d1= (A + B) d2 = (A^2 + B)^(1/2) d3 = (A^3 + B)^(1/3) d4 = (A^4 +
B)^(1/4) d5 = (A^5 + B)^(1/5)

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