Hi guys, need help with this question please:
The first term of a geometric series is 8. The sum of its first 10 terms is 1/8 of the sum of the reciprocal of these terms. Find the common ratio.
You have $\displaystyle \frac{8(1 - r^{10})}{1 - r} = \frac{1}{64} \frac{1 - \frac{1}{r^{10}}}{1 - \frac{1}{r}}$
My advice is to multiply the numerator and denominator of the right hand side of this equation by r^10. Then factorise the denominator, then look for common factors to cancel, simplify etc.
I end up with the simple equation $\displaystyle r^9 = - \frac{1}{8^3}$