Expected time to fill a table [duplicate]

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Say I have a table of numbers 1-6. I throw a 6 sided die a number of times. Each time I get a number I have not already had, I mark it in the table. What is the expected number of times to throw the dice to fill out the table?

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If $X$ denotes the number of throws that are needed then you can write: $$X=1+X_{1}+X_{2}+X_{3}+X_{4}+X_{5}$$ where $X_{i}$ has geometric distribution with parameter $\frac{6-i}{6}$.