Fraction series tending to $π / 2$

By Chris Park on Wednesday, September 26, 2001 - 06:02 am:

What is the value of T_n (n^th term) of this sequence as n goes to infinity?

2x2

1x3

2x2x4

1x3x3

2x2x4x4

1x3x3x5

2x2x4x4x6

1x3x3x5x5

2x2x4x4x6x6

1x3x3x5x5x7

Thank you!

By Arun Iyer on Thursday, September 27, 2001 - 08:06 pm:

lim_{n \to \infty} (\frac{2 \times 2 \times 4 \times 4 \times 6 \dots (2 n) (2 n)}{1 \times 3 \times 3 \times 5 \times 5 \dots (2 n - 1) (2 n - 1) (2 n + 1)}) = \frac{π}{2}

This is called the Wallis formula.

love arun

By The Editor

This gives one way of calculating

π

It takes a while to converge, but it would be reasonably easy to set up a short program to do it.