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If a < 1 and b < 1 , then the sum of the series a a + b + a 2 a 2 + b 2 + a 3 a 3 + b 3 + … is

Options

  1. Aa 1 - a + a b 1 - a b
  2. Ba 2 1 - a 2 + a b 1 - a b
  3. Cb 1 - b + a 1 - a
  4. Db 2 1 - b 2 + a b 1 - a b

Correct answer

B. a 2 1 - a 2 + a b 1 - a b

Step-by-step solution

We have, a < 1 ,   b < 1 ∴       a b = a b < 1 Now, a a + b + a 2 a 2 + b 2 + a 3 a 3 + b 3 + …   =       a 2 + a 4 + a 6 + … + a b + a b 2 + a b 3 + … =   a 2 1 - a 2 + a b 1 - a b

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