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Homework Statement
I have trouble with the summation notation.
[itex]\sum_{i=0}^{k}\binom{k}{i}f_{n+i}[/itex]
How do I write this as a sequence based on the definition of Fibonacci sequence?
Homework Equations
Definition:
f(0)=0
f(1)=1
f(n)=f(n-1) + f(n-2) for n>=2
Example:
f(2) = f(1) + f(0) = 1+0 = 1
f(3) = f(2) + f(1) = 1+1 = 2
f(4) = f(3) + f(2) = 2+1 = 3
f(5) = f(4) + f(3) = 3+2 = 5
and so on
The Attempt at a Solution
I know how to write:
[itex]\sum_{i=1}^{n}(i) = 1+2+3+...+n [/itex]
but I do not understand how to write the following Fibonacci sequence:
[itex]\sum_{i=0}^{k}\binom{k}{i}f_{n+i}[/itex]
Can someone show me how to write this as an expanded version or give me an example how to do this?
Thank you.