The sum of an infinite geometric series with first term 1 and ratio 1/2 is?
A
1
B
2
C
3
D
4
Correct Answer: Option B — 2
Explanation:
Sum = a/(1-r) = 1/(1-0.5) = 1/0.5 = 2. The series 1+1/2+1/4+1/8+... converges to 2. The condition |r|<1 must hold for convergence. Infinite geometric series appear in competitive exam algebra and also model real-world phenomena like bouncing balls and repeating decimal conversions.