Okay, so I have the following thing:
$$\sum_{i=1}^a F_{2i}=F_{2a+1}-1 $$
It's to do with Fibonacci sequence.
I can do the basis step of MI fine (proving for $a = 1$)
However the inductive step has left me stumped. I don't know how to transform it to prove it, and none of the other answers on this site appear to be similar, unfortunately. Any help?
Write down what you want, use the resursive definition of sum, use the induction hypothesis, use the recursion formula for Fibonacci numbers, done:
$$\sum_{i=1}^{a+1} F_{2i} = \sum_{i=1}^{a} F_{2i} +F_{2(a+1)}=F_{2a+1}-1+F_{2a+2}=F_{2a+3}-1$$