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 Feb15 awarded Popular Question Jul2 awarded Curious Jul25 comment Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? and RonGordon's explicit form helps me get to that conclusion so I accepted his answer. Jul25 comment Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? @HarishKayarohanam Thanks anyway. But all I want to look for is the form I provide above(in my comment) which appeared in that paper. Jul25 comment Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? btw the confusing form appeared at nearly the end of page 4 of this paper projecteuclid.org/… Jul25 accepted Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? Jul25 comment Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? @RonGordon Thanks. Jul25 comment Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? @RonGordon Just figured it out it is 1 + nC1(1/x) + (n+1)C2(1/x^2) + (n+2)C3(1/x^3) + ... Jul25 comment Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? How about the - sign is taking out from each coeff e.g. the second coeff is -nC1 etc. Is it possible? Jul25 asked Could you please explain How to expand $(1 - \frac1x)^{-n}$ into a sum of powers of $x$? May22 accepted What is the mathematical definition of index set? May22 asked What is the mathematical definition of index set? May18 comment How to calculate the probability mass function of $X_N$, the number of people getting back their own hat I think maybe you could show how to get the pmt of N=4 as an example. May18 comment How to calculate the probability mass function of $X_N$, the number of people getting back their own hat Thank you. But I think what you just did was rewriting my question. Also n is from 0. Means no one getting there own hat. May18 revised How to calculate the probability mass function of $X_N$, the number of people getting back their own hat edited body; edited title May18 comment How to calculate the probability mass function of $X_N$, the number of people getting back their own hat Yes, I will change the $X$ to $X_N$, where $X_n$ could integers be from 0 to N. May18 comment How to calculate the probability mass function of $X_N$, the number of people getting back their own hat Right it should be pmf. May18 revised How to calculate the probability mass function of $X_N$, the number of people getting back their own hat edited body; edited title May18 comment How to calculate the probability mass function of $X_N$, the number of people getting back their own hat (Assume everyone got a hat before exchange.) May18 asked How to calculate the probability mass function of $X_N$, the number of people getting back their own hat