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sequence defined as such: $$ \left(u_k ight) = egin{cases} u_ = \ u_k = u_{k- } + u_{k- } \cdot rac{ }{n} \end{cases}\quad ext{with}\... sequences-and-series limits recurrence-relations exponential-function closed-form asked hours ago eigenpussy silver badge bronze badges votes answer views prove, by induction
, that $arphi^{n+ } = arphi \cdot f_{n+ } + f_n$ for all natural numbers $n$. fibonacci rules: egin{align*} f_ = && f_ = && f_{n+ } = f_n + f_{n+ } \end{align*} the first ten terms of the fibonacci sequence are , , , , , , , , , . if ... discrete-mathematics proof-writing induction proof-explanation...
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