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Its known that the Bellman equation in recursive macroeconomics is used for the following problems:

$$\sum_{t=1}^\infty\beta^tU(c_t)$$ $$s.t. c_t+k_{t+1}=f(k_t)$$ $$k_0>0$$

Im wondering if we can apply the bellman equation to problems with finite horizon. The reason why I ask is because it would be considerably easier solving a bellman for a policy function than to solve for these values sequentially.

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