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Wallis product: (π/2) = product of [2n/(2n-1)] × [2n/(2n+1)] for n=1,2,3,...

Answer: π/2.

  • A 2/π
  • B π/2
  • C π
  • D 4/π

Correct answer: B. π/2

Explanation: Wallis derived this from ∫₀<sup>π/2</sup>sin<sup>2n</sup>x dx evaluated two ways. The infinite product (2/1)(2/3)(4/3)(4/5)(6/5)(6/7)... converges to π/2, giving a beautiful product representation of π.

xyabArea = integral of f(x) dxRectangles approximate the area (Riemann sum)

The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.

Concept context

Indefinite and definite integrals, areas under curves

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