Question 25
Let $a_n = \{\sqrt{n}\} - \{\sqrt{n+1}\} + \{\sqrt{n+2}\} - \{\sqrt{n+3}\}$, where $\{x\}$ denotes the fractional part of the real number $x$.
a) Prove that $a_1 \gt 0.2$.
b) Prove that $a_n \lt 0$, for infinitely many $n$, and $a_n \gt 0$, for infinitely many $n$.
a) Prove that $a_1 \gt 0.2$.
b) Prove that $a_n \lt 0$, for infinitely many $n$, and $a_n \gt 0$, for infinitely many $n$.