csat-suneung 2009 Q21

csat-suneung · South-Korea · csat__math-humanities 3 marks Geometric Sequences and Series Sum of an Infinite Geometric Series (Direct Computation)
For two infinite geometric sequences $\left\{ a _ { n } \right\} , \left\{ b _ { n } \right\}$ with the same common ratio, $a _ { 1 } - b _ { 1 } = 1$, $\sum _ { n = 1 } ^ { \infty } a _ { n } = 8$, and $\sum _ { n = 1 } ^ { \infty } b _ { n } = 6$. Find the value of $\sum _ { n = 1 } ^ { \infty } a _ { n } b _ { n }$. [3 points] 
For two infinite geometric sequences $\left\{ a _ { n } \right\} , \left\{ b _ { n } \right\}$ with the same common ratio, $a _ { 1 } - b _ { 1 } = 1$, $\sum _ { n = 1 } ^ { \infty } a _ { n } = 8$, and $\sum _ { n = 1 } ^ { \infty } b _ { n } = 6$. Find the value of $\sum _ { n = 1 } ^ { \infty } a _ { n } b _ { n }$. [3 points]
Paper Questions
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