Question
What is the value of (1-1/9) (1-1/16) (1-1/25) … (1-1/10000) is?
A. 9999
B. 10000
C. 202/300
D. 101/300
Answer: C. 202/300
Solution:
The Given series is:
(1-1/9) (1-1/16) (1-1/25) … (1-1/10000)
=(3^2-1)(4^2-1)(5^2-1)….(100^2-1)/(3^2*4^2*5^2……..100^2)
=(3–1)(3+1)(4–1)(4+1)(5–1)(5+1)…..(100–1)(100+1)/(3^2*4^2*5^2……100^2)
=(2*4)(3*5)(4*6)…..(99*101)/(3^2*4^2*5^2….100^2)
=2*101/(3*100)
=202/300
Hence, (1-1/9) (1-1/16) (1-1/25) … (1-1/10000) = 202/300.