WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Some Identities for an Alternating Sum of Fibonacci and Lucus Numbers of Order k
Authors: Sukanya Somprom, Waitaya Nimnual, Wathcharapong Hongthong
Abstract: In this paper, we defined $$F^{(k)}_{n}$$ be the Fibonacci of order $$k$$ and $$L^{(k)}_{n}$$ be the Lucas number of order
$$k$$. We presented some of their new identities as well as some results of relation for an alternating sum between
Fibonacci and Lucas number of order $$k$$ as follow;
$$\displaystyle\sum\limits_{i=0}^n (-1)^{i}m^{n-1}(mL^{(k)}_{i+1}+((m-2)^2-4)F^{(k)}_{i}-2m^2F^{(k)}_{i-1}-m\displaystyle\sum\limits_{j=3}^k jF^{(k)}_{i-j+2}=(-1)^nm(F^{(k)}_{n+1}-2F^{(k)}_{n})$$.