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Given: f(x)=x3+3x−9
The sum of infinite GP = max value of f(x) on [−2, 3]
The difference between first two terms = f′(0)
Step 1: f(x) is increasing ⇒ Max at x=3
f(3)=27⇒a1−r=27
Step 2: f′(x)=3x2+3⇒f′(0)=3
⇒ a(1−r)=3
Step 3: Solve:
a=27(1−r)
⇒27(1−r)2=3⇒(1−r)2=19⇒r=23
✅ Final Answer: r=23
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