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Series 1 + r + r2 + r3 + . . . . . ∞ is

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UP TGT Mathematics 2013 Official Paper
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  1. convergent for |r| < 1
  2. divergent for r ≥ 1
  3. oscillatory for r ≤ -1
  4. all of these

Answer (Detailed Solution Below)

Option 4 : all of these
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Detailed Solution

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Given series is 1 + r + r2 + r3 + . . . . . ∞

  1. |r| < 1 the series sum approaches to a fixed value hence it is convergent.
  2. |r| > 1, the sum of series goes on increasing hence it is divergent.
  3. r ≤ -1, the series does not approach a fixed value, hence it is oscillatory.
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