Iný výpočet pre $F_{2n}=\sum_{k=0}^n \binom nk F_k$
Posted: Tue Apr 25, 2023 2:39 pm
Sumu $F_{2n}=\sum_{k=0}^n \binom nk F_k$ sme na cviku odvodili pomocou matíc - padla aj otázka na iné dôkazy tej istej sumy.
Pridám aspoň nejaké linky:
Pridám aspoň nejaké linky:
- Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
- Inductive proof of the identity $\binom{n} {0} F_0+\binom{n}{1} F_1+\binom{n}{2} F_2+\cdots +\binom{n}{n} F_n=F_{2n}$
- Generating function of even Fibonacci numbers