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In this paper, we study the advantages of using range extension cooperative transmission (CT) in multi-hop energy harvesting wireless sensor networks (EH-WSNs) from the network layer perspective. EH-WSNs rely on harvested energy, and therefore, if a required service is energy-intensive, the network may not be able to support the service successfully. We show that CT networks that utilize both range extension CT and non-CT routing can successfully support services that cannot be supported by non-CT networks. For a two-hop toy network, we show that range extension CT can provide better services than non-CT. Then, we provide a method of determining the supportable services that can be achieved by using optimal non-CT and CT routing protocols for EH-WSNs. Using our method and network simulations, we justify our claim that CT networks can provide better services than non-CT networks in EH-WSNs.