Summation of the product of certain functions and generalized Fibonacci numbers
In this paper, we derived the summation< mml: mstyle displaystyle=" true">∑ i= 0 nf (i) U i
and< mml: mstyle displaystyle=" true">∑ i= 0∞ f (i) U i for certain functions f (i), where {U i} is
the generalized Fibonacci sequence defined by U n+ 2= pU n+ 1+ qU n for all p, q∈ Z+ and
for all non-negative integers n with the seed values U 0= 0, U 1= 1.
and< mml: mstyle displaystyle=" true">∑ i= 0∞ f (i) U i for certain functions f (i), where {U i} is
the generalized Fibonacci sequence defined by U n+ 2= pU n+ 1+ qU n for all p, q∈ Z+ and
for all non-negative integers n with the seed values U 0= 0, U 1= 1.
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