Zaymiey

📐 Mathematics  ·  Sequences and Series  ·  JEE

Sum: 1 - 1/2 + 1/4 - 1/8 + ... to infinity =

Answer: 2/3.

  • A 2/3
  • B 1/2
  • C 3/4
  • D 1/3

Correct answer: A. 2/3

Explanation: Infinite GP: first term a=1, common ratio r=−1/2 (|r|<1). Sum = a/(1−r) = 1/(1+½) = 1/(3/2) = 2/3.

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 →