Problem 199 (difficulty: 3/10)

Is there a sequence of irrational numbers converging to (a) 1, (b) \(\displaystyle \sqrt 2 \)?

Solution:

(a) \(\displaystyle 1+\frac{\sqrt 2}n\)    (b) \(\displaystyle \left(1+\frac1n\right)\sqrt 2\).

Give me another random problem!