Question

If you choose a p that is any small positive number ,then (5/6)^n < p is true for all sufficiently large value of n. To answer this question find a value N for which n > N, then (5/6)^n < p for p = 0.000001. Explain why this value of N is not unique. It is customary to summarize this situation by writing lim_{n rightarrow infty}\frac{ 5 }{ 6 }^{n} = 0

Answer 1

\[\lim_{n \rightarrow \infty}\frac{ 5 }{ 6 }^{n} = 0\]

Answer 2

"Explain why this value of N is not unique."

Because larger values of n make (5/6)^n even smaller.