If you are going to ask the sort of question with so many subscripts, the please learn to use LaTeX.
I cannot read this question.
{Fsubn} n>=o is defined Fsub0=0, Fsub1=1, fsub(n+2) = fsub(n+1) + fsub(n) [fibonacci]. Show for all n>=0:
Sum [(m, k=0) F^2(subk)] = Fsubm * Fsub(m+1).
So I got this far:
Induction shows 0 to work.
Sum + (m+1)^2 = Fsubm + Dsub(m+1) + (m+2)^2 = Fsub(m+1) * Fsub(m+2)
Fsub(m+1) * Fsub(m+2) = Fsub(m+1) * [Fsub(m+1) + Fsubm] = Fsubm * Fsub(m+1) + Fsub(m+1) * Fsub(m+1)
As far as I got.
Ya agree with Plato here, kinda hard to know whats going on. Use the examples on the left below and put them between the [tex] [/ math] tags (without the space between the / and math) to make them look like the right hand side.
F_m =
F_{m+1} =
\sum_{m=1}^{\infty} =