Chapter 13, Problem 16E

Fact: If we make a list of any 10 consecutive Fibonacci numbers, the sum of all these

numbers divided by 11 is always equal to the seventh number on the list.

a. Verify this fact for the list $F_1$, $F_2$,..., $F_{10}$.

b. Using the list $F_N$, $F_{N+1}$,..., $F_{N+9}$, write this fact as a mathematical formula.