Question
prove that the integral part of binomial expention is even
(5√5 + 11)2n+1
Joshi sir comment
Let x = (5√5 + 11)2n+1 and y = (5√5 - 11)2n+1
so x*y = 42n+1 = even number
similarly x - y = integer
if we consider the value of y , it will be (5*2.3-5)2n+1 = (0.5)2n+1 = fraction number less than 1 (approx)
so definitely y will be the fractional part of x, and difference of x and y is even so integer part of x will be even