Answer by DanielV for Using induction to prove an exponential lower bound for...
Induct on n:Base case, n=6:$$F_6 >= 2^{0.5n}$$$$13 >= 2^3$$Inductive assumptions:$$F_n >= 2^{0.5n}$$$$F_{n-1} >= 2^{0.5(n - 1)}$$$$n > 6$$Recursive case:$$F_{n+1} >= 2^{0.5(n +...
View ArticleAnswer by André Nicolas for Using induction to prove an exponential lower...
It is almost finished. But for the induction to work, we also need to verify the inequality for $n=7$.After that, all we need to do is to prove that$$2^{\frac{n}{2}}+2^{\frac{n-1}{2}}\gt...
View ArticleAnswer by Dennis Meng for Using induction to prove an exponential lower bound...
Hint: $2^{\frac{n}{2}} + 2^{\frac{n-1}{2}} < 2^{\frac{n}{2}} + 2^{\frac{n}{2}}$.
View ArticleUsing induction to prove an exponential lower bound for the Fibonacci sequence
The Fibonacci sequence $F_0, F_1, F_2,...,$ is defined by the rule:$$F_0=0, F_1=1, F_n=F_{n-1}+F_{n-2}$$ Use induction to prove that $F_n\geq2^{0.5n}$ for $n\geq 6$So far I have done the basis step...
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