MathDB

30

Part of PEN G Problems

Problems(1)

G 30

Source:

5/25/2007
Let α=0.d1d2d3⋯\alpha=0.d_{1}d_{2}d_{3} \cdots be a decimal representation of a real number between 00 and 11. Let rr be a real number with ∣r∣<1\vert r \vert<1. [*] If α\alpha and rr are rational, must ∑i=1∞diri\sum_{i=1}^{\infty} d_{i}r^{i} be rational? [*] If ∑i=1∞diri\sum_{i=1}^{\infty} d_{i}r^{i} and rr are rational, α\alpha must be rational?
inductionblogsirrational numberIrrational numbers