MCQ practice · SSC Higher Mathematics Board questions · Chapter 7: Infinite Series
If the sum to infinity of the infinite geometric series a + ab + ab² + … exists, which is correct for b?
Think it through first, then pick an option.
- a b = −1
- b |b| > 1
- c |b| < 1
- d b = 1
Answer and explanation
Correct answer: c |b| < 1
The condition for a sum is |b| < 1 for the common ratio b.
Why the other options are wrong
- a b = −1: For b = −1 the series is a − a + a − …, with no sum.
- b |b| > 1: For |b| > 1 the terms keep growing; there is no sum.
- d b = 1: For b = 1 the series is a + a + a + …, Sₙ = na, with no sum.
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