Standard +0.8 This question requires students to equate formulas for S_∞ and S_n, manipulate the resulting equation algebraically to isolate r^6, then recognize that taking the sixth root yields r = ±1/√k. While the setup is standard, the algebraic manipulation and final form require careful handling of powers and roots beyond routine exercises.
10. In a geometric series the common ratio is \(r\) and sum to \(n\) terms is \(S _ { n }\)
Given
$$S _ { \infty } = \frac { 8 } { 7 } \times S _ { 6 }$$
show that \(r = \pm \frac { 1 } { \sqrt { k } }\), where \(k\) is an integer to be found.
10. In a geometric series the common ratio is $r$ and sum to $n$ terms is $S _ { n }$
Given
$$S _ { \infty } = \frac { 8 } { 7 } \times S _ { 6 }$$
show that $r = \pm \frac { 1 } { \sqrt { k } }$, where $k$ is an integer to be found.\\
\hfill \mbox{\textit{Edexcel Paper 2 Q10 [4]}}