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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

`ninN`

,

`F_(1)+F_(3)+F_(5)+dotsF_(2n-1)=F_(2n).`