Multiple choice general knowledge math & puzzles

Value of (31/4.91/8.271/16………… to infinity) is

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The infinite product 3^(1/4) × 9^(1/8) × 27^(1/16) × ... = 3^(1/4 + 2/8 + 3/16 + ...). The exponent is sum of n/2^(n+1) for n=1 to infinity. Using the formula for sum of n/2^n = 2, we get exponent = 1/2 = 1. Therefore product = 3^1 = 3. This uses infinite series and geometric progression.

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