[1KG]Find two examples of series \( f(t)=β_{k=0}^β a_ k t^ k\) with \(a_ k{\gt}0\) and with radius of convergence \(r\) positive and finite, such that
\(f(r){\lt}β\)
\(f(r)=β\)
[1KH]βΊβ»
