Question

Express the product (1−1/2^2)(1−1/3^2)(1−1/4^2)···(1−1/21^2) as a fraction a/b, where a and b are relatively prime positive integers.

Answer 1

22/42 = 11/21

Answer 2

How? I can't see the pattern.

Answer 3

1 - 1/k^2 = (k^2-1)/k^2 = (k-1)(k+1)/k^2
write out terms up to n and you will see how the factors cancel.
The product is (n+1)/(2n)

Answer 4

Thank you