Prove that $P(r)$ is a strictly decreasing function of $r$ when $r$ > $-1$ and that $\lim \limits_{x \to -1+}$ $P(r)=\infty$, $\lim \limits_{x \to \infty}$ $P(r) = -1 < 0$.
$P(r) = -a + $$\sum_{i=1}^n b_i(1+r)^{-i}$
Is this something where I try and take the derivative of this and use monadicity theorem? Thanks for help in advance
do you mean $\lim_{r \to 1+}$ instead of $\lim_{x \to 1+}$? you take the derivative and see it's strictly negative given $r > -1$, so you can conclude the function is strictly decreasing.