Use the definition of convergent to prove :
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Originally Posted by flower3 Use the definition of convergent to prove : Yes, what have you done? What is the definition of convergence for a sequence?
For this particular problem, you might consider taking the logarithm of every number in the sequence and looking at that new sequence.
. Obviously , so we need to only prove that .
For n > 1 we have . So we can let where is some positive quantity depending on n.
So . Now, it is clear from the binomial theorem that .
Can you show that goes to 0 and so goes to 1?
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