Let {Xn}, {yn} be real sequences and b,x,y be real numbers.

Prove (using limit theorems)

If Xn goes to X and Yn goes to Y as n goes to infinity, then

i)lim (Xn + Yn) = X+Y

ii)lim (bXn) = bX

iii) lim (XnYn) = XY

(all limits n going to infinity)

Thanks