MCQ practice · SSC Higher Mathematics Board questions · Chapter 7: Infinite Series
What is the sum to infinity of the infinite geometric series 0.2 + 0.02 + 0.002 + …?
Think it through first, then pick an option.
- a 2/11
- b 2/9
- c 9/2
- d 11/2
Answer and explanation
Correct answer: b 2/9
a = 0.2, r = 0.1; S∞ = 0.2/(1 − 0.1) = 0.2/0.9 = 2/9.
Why the other options are wrong
- a 2/11: 2/11 would need 1 + r = 1.1 in the denominator; it is 1 − r = 0.9.
- c 9/2: 9/2 is the reciprocal of the right value; the sum is just above a, near 0.2.
- d 11/2: 11/2 = 5.5 is far too large; the sum is a little above 0.2, about 0.22.
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