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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

Compute ∑n=1∞Fn2n\displaystyle\sum_{n=1}^\infty \frac{F_n}{2^n}, where F1=F2=1F_1 = F_2 = 1 and Fn+2=Fn+1+FnF_{n+2} = F_{n+1} + F_n.