Zaymiey

📐 Mathematics  ·  Sequences and Series  ·  JEE

Sum of the series: 1 + 2x + 3x² + 4x³ + ... to infinity (|x| < 1) =

Answer: 1/(1-x)².

  • A 1/(1-x)²
  • B 1/(1-x)
  • C x/(1-x)²
  • D 1/(1-x) + 1

Correct answer: A. 1/(1-x)²

Explanation: This is the derivative form: d/dx [sum x<sup>n</sup>] = sum n x<sup>n-1</sup>, so sum (n+1)x<sup>n</sup> = 1/(1-x)². Replacing n+1 with the lead: sum from n=1 is (1-x)<sup>-2</sup> = 1/(1-x)².

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

Read the full Sequences and Series notes →