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A coupled-cluster approach for systems of $N$ bosons in external traps isdeveloped. In the coupled-cluster approach the exact many-body wavefunction isobtained by applying an exponential operator $\exp{T}$ to the groundconfiguration $|\phi_0>$. The natural ground configuration for bosons is, ofcourse, when all reside in a single orbital. Because of this simple structureof $|\phi_0>$, the appearance of excitation operators $T=\sum_{n=1}^N T_n$ forbosons is much simpler than for fermions. We can treat very large numbers ofbosons with coupled-cluster expansions. In a substantial part of this work, weaddress the issue of size consistency for bosons and enquire whether truncatedcoupled-cluster expansions are size consistent. We show that, in contrast tothe familiar situation for fermions for which coupled-cluster expansions aresize consistent, for bosons the answer to this question {\it depends} on thechoice of ground configuration. Utilizing the natural ground configuration,working equations for the truncated coupled-cluster with $T=T_1+T_2$, i.e.,coupled-cluster singles doubles (CCSD) are explicitly derived. Finally, anillustrative numerical example for a condensate with up to N=10000 bosons in anharmonic trap is provided and analyzed. The results are highly promising.Comment: 35 pages, 3 figure

Coupled-cluster theory for systems of bosons in external traps