This is my question

(a) By comparing consecutive terms, prove the unimodularity property of the binomial co- efficients. That is, show that (8) ( in/ 2 1 + 1 ) > > . . . > (b) Let p E (0, 1], and define fp(k) = (2)p*(1 -p)"-k (this is an important quantity in probability!). Which value of k E N maximizes fp(k)