tmua 2023 Q18

tmua · Uk · paper1 1 marks Geometric Sequences and Series Geometric Series with Trigonometric or Functional Terms

You are given that
$$S = 4 + \frac { 8 k } { 7 } + \frac { 16 k ^ { 2 } } { 49 } + \frac { 32 k ^ { 3 } } { 343 } + \cdots + 4 \left( \frac { 2 k } { 7 } \right) ^ { n } + \cdots$$
The value for $k$ is chosen as an integer in the range $- 5 \leq k \leq 5$
All possible values for $k$ are equally likely to be chosen.
What is the probability that the value of $S$ is a finite number greater than 3 ?

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You are given that

$$S = 4 + \frac { 8 k } { 7 } + \frac { 16 k ^ { 2 } } { 49 } + \frac { 32 k ^ { 3 } } { 343 } + \cdots + 4 \left( \frac { 2 k } { 7 } \right) ^ { n } + \cdots$$

The value for $k$ is chosen as an integer in the range $- 5 \leq k \leq 5$

All possible values for $k$ are equally likely to be chosen.

What is the probability that the value of $S$ is a finite number greater than 3 ?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20