the question is asking me to Prove that $d_n$ is constant in the case of compound interest.
What I know so far and have tried is the formula for compound interest is $a(t)=(1+i)^t$ and I think that $d_n$ is possibly supposed to represent the discount maybe. But I there is no $d_n$ in the formula for compound interest so I am confused on how I am supposed to prove this.
$$ a(n) = P (1+i)^n $$
$$ d_n = \frac{P (1+i)^n -P (1+i)^{n-1} }{P (1+i)^n } = 1-(1+i)^{-1} $$ which does not depend on $n$