formula for coefficient of y^n?

Question

Give a formula for the coefficient of y^n in the expansion of (y + (2/y))^100, where k is a nonnegative integer.

Answer 1

The general term in the expansion of
(y + (2/y))^100
is

(100 above k) · y^(100-k) · (2/y)^k =

(100 above k) · y^(100-k) · 2^k · y^(-k) =

100!/(100-k)!·k! · 2^k · y^(100-2k)

... are you told what exactly n should be?

Because if n = 50, say, than
100-2k should equal 50, i.e. k = 25 and then the term is

100!/75!·25! · 2^25 · y^50

and the coefficient of y^50 is 100!/75!·25! · 2^25.

Answer 2

I would like to point out one missing detail from the very good first answer. Namely, k has to be an integer and hence the formula only gives the coefficient for EVEN values of n (= 100 -2k).

To make the answer complete, note that the coefficient for the y^n term is zero if n is an odd integer.