(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant 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

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Summation notation Fibonacci

**Physics Forums | Science Articles, Homework Help, Discussion**