Question

2. If X = {4^n- 3n-1:n belongs to N) and y = 19(n-1): n belongs to N), then XUY equals
(a) X
(b) Y
(C)N​

Answer 1

Answer:

4n=(3+1)n = nC0 + nC1*31 + nC2 * 32 + nC3 * 33 +........+ nCn * 3n,

Take nC0 and nC1*3 on left hand side,

x=nC2 *9 + nC3*27...... + nCn *3n,

hence x is always divisible by 9,

So you can write x= 9*(nC2 + nC3*3......+ nCn *3n-2) = 9*z, where z is an integer,

z will only have specific integer values. Hence zUN = N, or XUY=Y

ATB