Waiting time in an immigration-birth process

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Could someone please verify that none of the four given choices are correct? Isn't the correct answer $$\frac 1{(\lambda + 4\beta)^2} + \frac 1{(\lambda + 5\beta)^2} + ... +\frac 1{(\lambda + (3+n)\beta)^2}?$$

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Yes. And yes. (And some irrelevant words.)