MediumPower & Taylor series

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.5 Power Series, #29 · Calculus · Power & Taylor series

In … the coefficient of … is the number of groups of…

In $(1 - x)^{- 1} = Σ x^{n}$ the coefficient of $x^{n}$ is the number of groups of $n$ friends that can be formed from 1 friend (not binomial—repetition is allowed). The coefficient is 1 and there is only one group—the same friend $n$ times.
(a) Describe all groups of $n$ friends that can be formed from 2 friends. (There are $n + 1$ groups.)
(b) How many groups of 5 friends can be formed from 3 friends?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.5 Power Series, #29

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