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Question 210026
JEE Mathematics · Hard

Sequences and Series: AGP MCQ

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AGPHardQuestion 210026

Question

The sum 1·1 + 2·2 + 3·4 + 4·8 + ... to n terms (arithmetico-geometric) where a_r = r·2^(r−1) is tricky. Instead: what is 1 + 2x + 3x² + 4x³ + ... for |x| < 1?
  1. A
    1/(1−x)
  2. B
    1/(1−x)²
    Correct
  3. C
    (1+x)/(1−x)²
  4. D
    x/(1−x)²

Correct answer

1/(1−x)²

Explanation

Differentiate the GP sum: d/dx[1/(1−x)] = 1/(1−x)² = 1 + 2x + 3x² + ... . This AGP sum formula is essential.

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