Write f1 f3 f5 f2n-1 in summation notation then show

Question

Question: 1. Write F₁ + F₃ + F₅ + ··· + F_2n-1 in summation notation. Then show that F₁ +F₃ +F₅ +···+F_2n-1 = F_2n.

2. Write F₂ +F₄ +F₆ +···+F_2n in summation notation. Then show that F₂ + F₄ +F₆ +···+F_2n = F_2n+1 -1.

3. Prove that F_3n is even.

4. Write F₁ - F₂ + F₃ - F₄ + ··· + F_2n-1 - F_2n in summation notation. Then show that F₁ -F₂ +F₃ -F₄ +···+F_2n-1 -F_2n = 1-F_2n-1.