Question 170
Let $Q_n(x) = 1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n!}$ for $n \ge 0$ integer and $x$ real.
Prove that we have $\frac{Q_n(b) - Q_n(a)}{b-a} \ge Q_{n-1}\left(\frac{a+b}{2}\right)$ for any $n \ge 1$ and $b \gt a \gt 0$.
Prove that we have $\frac{Q_n(b) - Q_n(a)}{b-a} \ge Q_{n-1}\left(\frac{a+b}{2}\right)$ for any $n \ge 1$ and $b \gt a \gt 0$.