Problem 2. For each
ninN
, let
F_(n)
be the
n^(th )
Fibonacci number. So,
F_(1)=F_(2)=1
, and for all
n>=2,F_(n+1)=F_(n)+F_(n-1)
. Prove that for each
,
F_(1)+F_(3)+F_(5)+dotsF_(2n-1)=F_(2n).