Further Pure Math 9-1 4PM1: Series Topical Past Paper Questions

(i) A geometric series $ G $ has first term $ (3 + \sqrt{3}) $ and common ratio $ r $. The second term of $ G $ is $ \sqrt{3} $. (a) Find, showing all your working, the exact value of $ r $. Give your answer in the form $ \frac{p+\sqrt{3}}{q} $ where p and q are integers to be fo…

(a) Use the factor theorem to show that $ (4x-1) $ is a factor of $$ \mathrm{f}(x)=64x^{3}-64x^{2}+3 $$ (b) Hence, or otherwise, find the exact roots of the equation $$ \mathrm{f}(x)=0 $$ A geometric series G has first term a and common ratio r. The third term of G is 9 and the s…

The nth term of a convergent geometric series is $ 8^{(1-2n)} $ Find the sum to infinity of the series. Give your answer in the form $ \frac{p}{q} $ where p and q are integers to be found.