MCQ practice · SSC Higher Mathematics Board questions · Chapter 7: Infinite Series
Regarding the series 0.032 + 0.00032 + 0.0000032 + …, which is correct?
- i. the series is a geometric series
- ii. the common ratio is 0.01
- iii. the sum to infinity is 32/99
Think it through first, then pick an option.
- a i and ii
- b i and iii
- c ii and iii
- d i, ii and iii
Answer and explanation
Correct answer: a i and ii
r = 0.00032/0.032 = 0.01; S∞ = 0.032/0.99 = 32/990, so iii is false.
Why the other options are wrong
- b i and iii: iii is false: the sum is 32/990 = 16/495, not 32/99; and ii is true, which is left out.
- c ii and iii: iii is false (the sum is 32/990) and i is true, which is left out.
- d i, ii and iii: iii is false: 0.032/0.99 = 32/990, not 32/99.
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