Hi Guys,

I hit a dead end while solving this problem. I haven't done Complex numbers so far, so I am not sure how to proceed.

By using logarithms, find approximately the difference between $\displaystyle \dfrac{a}{1 - r}$ and $\displaystyle \dfrac{a(1 - r^n)}{1 - r}$ where,

$\displaystyle a = 2, r = -0.7, n = 1001$

I used the difference formula,

$\displaystyle

D = \dfrac{ar^n}{r - 1}

$

and substituting for a, r and n, I got,

$\displaystyle D = \dfrac{2(-0.7)^{1001}}{1.7}$

But for the -0.7 I could have used the logarithm identities to solve this. But I can't take $\displaystyle log -0.7$. The required answer is $\displaystyle -1.032 \times 10^{-155}$

How do I proceed? Thanks again for your help!

Edit:

I went back and calculated $\displaystyle S$ and $\displaystyle S_{\infty}$ individually, They are both identical $\displaystyle =1.176$. Hence the difference would be 0. Is the textbook answer wrong?