JEE Main 2024 Mathematics question
If the range of , θ ∈ R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the common ratio is , is equal to .
Answer: 96
Solution
With s = sin²θ, f = 1 + 2(1 − s)/(s² − s + 1) takes values from 1 (s = 1) up to 3 (s = 0), so α = 1, β = 3. The sum is 64/(1 − 1/3) = 96.