Question

Find a if the 17th and 18th terms of the expansion of (2+a)^50 are equal

Answer 1

if i am no mistaken the 17 term is
\[\dbinom{50}{16}2^{16}a^{34}\]

Answer 2

and similarly 18 term is
\[\dbinom{50}{17}2^{17}a^{33}\] so i guess we can set them equal and solve

Answer 3

\[\dbinom{50}{16}2^{16}a^{34}=\dbinom{50}{17}2^{17}a^{33}\]
\[\dbinom{50}{16}a=\dbinom{50}{17}2\]

Answer 4

and so
\[a=\frac{2\dbinom{50}{17}}{\dbinom{50}{16}}\] whatever that is