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📐 Mathematics  ·  Sequences and Series  ·  JEE

The coefficient of x<sup>n</sup> in the expansion of 1/(1-x)² is:

Answer: n+1.

  • A n
  • B n+1
  • C n(n+1)/2
  • D 2n

Correct answer: B. n+1

Explanation: Use negative binomial: 1/(1−x)² = (1−x)<sup>−2</sup> = Σ C(n+1,1) xⁿ = Σ (n+1)xⁿ. Coefficient of xⁿ is (n+1).

Each bar grows by the common difference d=3a1=2a2=5a3=8a4=11d=3

Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.

Concept context

Arithmetic progressions, geometric progressions, and sums

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