How do we multiply infinite fractions?

Calculus Level 3

True or False?

1 2 × 2 3 × 3 4 × ⋯ = 1 × 2 × 3 × ⋯ 2 × 3 × 4 × ⋯ \dfrac12 \times\dfrac23\times \dfrac34 \times\cdots = \dfrac{1\times2\times3\times\cdots}{2\times3\times4\times\cdots}

False True

Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

On LHS we can go on canceling so the answer is 1.
The RHS we divide (1 to infinity) by (2 to infinity) = infinity divided by infinity, not defined.

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LHS tens to 0 and not 1

Krutarth Patel - 5 months, 2 weeks ago

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